arXiv subjects

Lukas Janssen

Publications and source records attributed to Lukas Janssen.

At least 19 recordsLinked to original sources

arXiv2026

Numerical evidence of a critical point in the (2+1)D SO(5) nonlinear sigma model with Wess-Zumino-Witten term

We develop an optimized continuous-field quantum Monte Carlo (QMC) algorithm to investigate the projected SO(5) nonlinear sigma model with a Wess-Zumino-Witten term, which describes half-filled Dirac fermions in 2+1 space-time dimensions akin to graphene and Yukawa coupled to a quintuplet of compatible mass terms. Our algorithm reduces the computational complexity to $O(\beta N_{\mathbf{q}} N_\phi^2)$, yielding a speedup of a factor of $N_\phi$ (the number of magnetic fluxes, i.e., system size) relative to prior works [1-4]. This advance enables us to simulate system sizes up to $N_\phi=140$ on the torus and $N_\phi=59$ on the sphere, far exceeding the maximum sizes previously accessed, and to map out the universal phase diagram of the model on both geometries. Most notably, we identify and characterize a critical point that separates an SO(5)-broken ordered phase at small coupling from an SO(5)-symmetric disordered phase at large coupling. The critical point becomes multicritical upon the inclusion of terms that break the SO(5) symmetry down to $\mathrm{U}(1) \times \mathrm{SU}(2)$, relevant for the deconfined phase transition between N\'eel antiferromagnetic and valence-bond-solid orders in quantum magnets. Our finding of a multicritical point in the phase diagram of the SO(5) nonlinear sigma model with Wess-Zumino-Witten term resolves the long-standing open question of its global structure, and our QMC algorithm opens a new avenue for systematic studies of projected Hamiltonians, ranging from correlated flat bands to fractional quantum (anomalous) Hall systems.

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arXiv2026

Emergent relativistic symmetry from interacting fermions on the honeycomb bilayer

We study the phase diagram of interacting spinless fermions on the honeycomb bilayer at charge neutrality using large-scale quantum Monte Carlo simulations. In the noninteracting limit, the low-energy spectrum features quadratically dispersing bands that touch at the corners of the hexagonal Brillouin zone. Weak to intermediate interactions induce a splitting of each of the quadratic band touching points into four Dirac points, located along high-symmetry directions of the reciprocal lattice. Strong interactions lead to the formation of a layer-polarized charge density wave, which spontaneously breaks the $\mathbb Z_2$ layer inversion symmetry and opens an insulating gap in the spectrum. We show that the semimetal-to-insulator quantum phase transition as a function of interaction is continuous and characterized by emergent relativistic symmetry. Our results for the values of the correlation-length exponent $\nu$, the order-parameter anomalous dimension $\eta_\phi$, and the fermion anomalous dimension $\eta_\psi$ agree with those of the theoretically predicted 2+1D Gross-Neveu-Ising universality class with eight two-component Dirac fermions within less than 5\%\ deviation. We also determine the crossover scale as a function of interaction strength between the nonrelativistic semimetal state at high temperatures, characterized by dynamical critical exponent $z = 2$, and the Dirac semimetal state at intermediates temperatures, characterized by $z=1$. Further reducing the temperature below the crossover scale at a fixed value of the interaction strength above the quantum critical point results in a classical ordering transition in the 2D Ising universality class.

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arXiv2025

Continuous order-to-order quantum phase transitions from fixed-point annihilation

A central concept in the theory of phase transitions beyond the Landau-Ginzburg-Wilson paradigm is fractionalization: the formation of new quasiparticles that interact via emergent gauge fields. This concept has been extensively explored in the context of continuous quantum phase transitions between distinct orders that break different symmetries. We propose a mechanism for continuous order-to-order quantum phase transitions that operates independently of fractionalization. This mechanism is based on the collision and annihilation of two renormalization group fixed points: a quantum critical fixed point and an infrared stable fixed point. The annihilation of these fixed points rearranges the flow topology, eliminating the disordered phase associated with the infrared stable fixed point and promoting a second critical fixed point, unaffected by the collision, to a quantum critical point between distinct orders. We argue that this mechanism is relevant to a broad spectrum of physical systems. In particular, it can manifest in Luttinger fermion systems in three spatial dimensions, leading to a continuous quantum phase transition between an antiferromagnetic Weyl semimetal state, which breaks time-reversal symmetry, and a nematic topological insulator, characterized by broken lattice rotational symmetry. This continuous antiferromagnetic-Weyl-to-nematic-insulator transition might be observed in rare-earth pyrochlore iridates $R_2$Ir$_2$O$_7$. Other possible realizations include kagome quantum magnets, quantum impurity models, and quantum chromodynamics with supplemental four-fermion interactions.

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arXiv2025

Exact nematic and mixed magnetic phases driven by competing orders on the pyrochlore lattice

Pyrochlore magnets are a paradigmatic example of three-dimensional frustrated systems and provide an excellent platform for studying a variety of exotic many-body phenomena, including spin liquids, nematic phases, fragmentation, and order by disorder. In recent years, increasing attention has been devoted to bilinear spin models on this lattice, where multiple magnetic phases can be degenerate in energy, often stabilizing unconventional magnetic states. In this work, we focus on one such model, parametrized by the interaction coupling $J_{z\pm}$, which defines a line in parameter space corresponding to the phase boundary between three distinct magnetic phases. Using a combination of analytical and numerical methods, we show that this model exhibits an order-by-disorder mechanism at low temperatures, giving rise to a \emph{mixed} magnetic phase. This represents the first realization of a $\mathbf{q}=0$ long-range-ordered phase in a pyrochlore magnet characterized by two distinct order parameters, which we denote as the $A_2 \oplus ψ_2$ phase. Furthermore, at $J_{z\pm} = 1/\sqrt{2}$, the model acquires a subextensive number of discrete symmetries, which preclude the stabilization of conventional long-range order and instead lead to the emergence of a novel nematic phase. We characterize this nematic phase, describe how its ground-state configurations are constructed, and analyze its stability at higher temperatures and under small deviations from $J_{z\pm} = 1/\sqrt{2}$.

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arXiv2025

Field-induced magnetic phases in the Kitaev candidate Na$_3$Co$_2$SbO$_6$

We report a rich anisotropic magnetic phase diagram of Na$_3$Co$_2$SbO$_6$, a previously proposed cobaltate Kitaev candidate, based on field- and temperature-dependent magnetization, specific heat, and magnetocaloric effect studies. At low temperatures, our experiments uncover a low-lying $j_{\textrm{eff}} = \frac{1}{2}$ state with an antiferromagnetic ground state and pronounced in-plane versus out-of-plane anisotropy. The experimentally identified magnetic phases are theoretically characterized through classical Monte Carlo simulations within an extended Kitaev-Heisenberg model with additional ring exchange interactions. The resulting phase diagram reveals a variety of exotic field-induced magnetic phases, including double-$\textbf{q}$, $\frac{1}{3}$-AFM, zigzag, and vortex phases.

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arXiv2025

Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids

We study the low-temperature phase diagram of quantum Kitaev-Heisenberg spin-orbital models with XXZ anisotropy on the honeycomb lattice. Within a parton mean-field theory, we identify three different quantum phases, distinguished by their symmetries. Besides a disordered spin-orbital liquid with unbroken U(1) x Z2 spin rotational symmetry, there are two orbital liquid phases characterized by spin long-range order. In these phases, the spin rotational symmetry is spontaneously broken down to residual U(1) and Z2 symmetries, respectively. The symmetric spin-orbital liquid features three flavors of linearly dispersing gapless Majorana fermions. In the symmetry-broken phases, one of the three Majorana excitations remains gapless, while the other two acquire a band gap. The transitions from the symmetric to the symmetry-broken phases are continuous and fall into the fractionalized Gross-Neveu-Z2* and Gross-Neveu-SO(2)* universality classes, respectively. The transition between the ordered phases is discontinuous. Using a renormalization group analysis based on the epsilon expansion, we demonstrate that the triple point in the phase diagram features fractionalized fermionic multicriticality with emergent SO(3) symmetry.

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arXiv2025

Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides

We investigate the phase diagram of moir\'e double bilayer transition metal dichalcogenides with ABBA stacking as a function of twist angle and applied pressure. At hole filling $\nu = 2$ per moir\'e unit cell, the noninteracting system hosts a Dirac semimetal with graphene-like low-energy bands in the moir\'e Brillouin zone. At small twist angles, the Fermi velocity is reduced and interactions dominate the low-temperature behavior. A strong-coupling analysis identifies insulating ferromagnetic and antiferromagnetic ground-state candidates, characterized by spin-density modulations set by the moir\'e scale. Using a realistic continuum model with long-range Coulomb interactions, we perform self-consistent Hartree-Fock calculations to study the competition between these states. Varying the twist angle or pressure drives a transition from a Dirac semimetal to an antiferromagnetic insulator, which breaks SU(2) spin rotation and two-fold lattice rotation symmetries. Within a renormalization group analysis of the most general symmetry-allowed low-energy field theory, we show that this semimetal-to-insulator transition is continuous and belongs to the (2+1)D relativistic Gross-Neveu-Heisenberg universality class with $N = 2$ four-component Dirac fermions. Finite heterostrain, relevant in realistic samples, induces a crossover from Gross-Neveu-Heisenberg universality at intermediate temperatures to conventional (2+1)D Heisenberg criticality at the lowest temperatures. Further decreasing the twist angle can cause a level crossing from the antiferromagnetic insulator into a ferromagnetic insulator with spin-split bands. Our results provide a comprehensive theoretical framework that complements and elucidates recent experiments in twisted double bilayer WSe$_2$.

cond-mat.mes-hall↗

arXiv2025

Direct probe of magnetic field effects on phonons by ultrasound propagation in a quasi-two-dimensional honeycomb magnet Na$_2$Co$_2$TeO$_6$

We study the phonon behavior of a Co-based honeycomb frustrated magnet Na$_2$Co$_2$TeO$_6$ under magnetic field applied perpendicular to the honeycomb plane. The temperature and field dependence of the sound velocity and sound attenuation unveil prominent spin-lattice coupling in this material, promoting ultrasound as a sensitive probe for magnetic properties. An out-of-plane ferrimagnetic order is determined below the Néel temperature $T_N=27$~K. A comprehensive analysis of our data further supports a triple-Q ground state of Na$_2$Co$_2$TeO$_6$. Furthermore, the ultrasound data were systematically compared to the thermal transport results from literature, to unveil the importance of phononic contribution to the observed transport behaviors.

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arXiv2025

Interaction-induced nematic Dirac semimetal from quadratic band touching: A constrained-path quantum Monte Carlo study

Electronic systems with quadratic band touchings, commonly found in two- and three-dimensional materials such as Bernal-stacked bilayer graphene, kagome metals, HgTe, and pyrochlore iridates, have attracted significant interest concerning the role of interactions in shaping their electronic properties. However, even in the simplest model of spinless fermions on a two-dimensional checkerboard lattice, the quantum phase diagram as a function of nearest-neighbor interaction remains under debate. We employ constrained-path quantum Monte Carlo simulations (CP-QMC) simulations to investigate the problem using a two-dimensional torus geometry. We cross-validate our results on small lattices by comparing them with density-matrix renormalization group calculations, finding quantitative agreement. In particular, we implement an improved optimization scheme within the CP-QMC simulations, enabling the identification of a bond-nematic Dirac semimetal phase that was found in tensor-network studies on cylindrical geometries, but remains inaccessible to Hartree-Fock mean-field methods. The CP-QMC approach makes it possible to establish the emergence of this phase in a geometry that preserves lattice rotational symmetry and permits extrapolation to the thermodynamic limit. Our results show that the quantum phase diagram of spinless fermions on the checkerboard lattice with nearest-neighbor repulsion features three interaction-induced phases at half filling: a quantum anomalous Hall insulator at weak coupling, a bond-nematic Dirac semimetal at intermediate coupling, and a site-nematic insulator at strong coupling.

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arXiv2025

Ferrimagnetism from quantum fluctuations in Kitaev materials

Ferrimagnetism appears in the temperature-field phase diagrams of several candidate Kitaev materials, such as the honeycomb cobaltates Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$. In a number of instances, however, the exact nature of the corresponding ground states remains the subject of ongoing debate. We show that general symmetry considerations can rule out candidate states that are incompatible with the observed ferrimagnetic behavior. In particular, we demonstrate that a ferrimagnetic response cannot be reconciled with a collinear zigzag ground state, owing to the combined time-reversal and translational symmetry inherent to that configuration. Instead, the observed behavior is fully compatible with the symmetries of noncollinear multi-$\mathbf q$ states, such as the triple-$\mathbf q$ discussed in the context of Na$_2$Co$_2$TeO$_6$. We exemplify this general result by computing the ferrimagnetic response of an extended Heisenberg-Kitaev-Gamma model with explicit sublattice symmetry breaking within linear spin-wave theory. If the model realizes a triple-$\mathbf q$ ground state, the calculated magnetization curve is well consistent with the low-temperature behavior observed in Na$_2$Co$_2$TeO$_6$. In this case, a finite magnetization remains in the zero-temperature limit as a consequence of quantum fluctuations, even if the $g$-factors on the different sublattices are identical. For a zigzag ground state, by contrast, the total magnetization vanishes both at zero and finite temperatures, independent of possible sublattice-dependent $g$-factors, as expected from the symmetry analysis. The implications of our general result for other Kitaev materials exhibiting ferrimagnetic behavior are also briefly discussed.

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arXiv2025

Gross-Neveu-XY quantum criticality in moiré Dirac materials

Two-dimensional van-der-Waals materials offer a highly tunable platform for engineering electronic band structures and interactions. By employing techniques such as twisting, gating, or applying pressure, these systems enable precise control over the electronic excitation spectrum. In moiré bilayer graphene, the tunability facilitates the transition from a symmetric Dirac semimetal phase through a quantum critical point into an interaction-induced long-range ordered phase with a finite band gap. At charge neutrality, the ordered state proposed to emerge from twist-angle tuning is the Kramers intervalley-coherent insulator. In this case, the transition falls into the quantum universality class of the relativistic Gross-Neveu-XY model in 2+1 dimensions. Here, we refine estimates for the critical exponents characterizing this universality class using an expansion around the lower critical space-time dimension of two. We compute the order-parameter anomalous dimension $η_φ$ and the correlation-length exponent $ν$ at one-loop order, and the fermion anomalous dimension $η_ψ$ at two-loop order. Combining these results with previous findings from the expansion around the upper critical dimension, we obtain improved estimates for the universal exponents in $2+1$ dimensions via Padé interpolation. For $N_\mathrm{f} = 4$ four-component Dirac fermions, relevant to moiré bilayer graphene, we estimate $1/ν=0.916(5)$, $η_φ=0.926(13)$, and $η_ψ=0.0404(13)$. For $N_\mathrm{f} = 2$, potentially relevant to recent tetralayer WSe$_2$ experiments, the Gross-Neveu-XY fixed point may be unstable due to a fixed-point collision at $N_\mathrm{f,c}$, with $N_\mathrm{f,c} = 1 + \sqrt{2} + \mathcal{O}(ε)$ in the expansion around the lower critical dimension.

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arXiv2025

Twist-tuned quantum criticality in moiré bilayer graphene

We argue that moiré bilayer graphene at charge neutrality hosts a continuous semimetal-to-insulator quantum phase transition that can be accessed experimentally by tuning the twist angle between the two layers. For small twist angles near the first magic angle, the system realizes a Kramers intervalley-coherent insulator, characterized by circulating currents and spontaneously broken time reversal and U(1) valley symmetries. For larger twist angles above a critical value, the spectrum remains gapless down to the lowest temperatures, with a fully symmetric Dirac semimetal ground state. Using self-consistent Hartree-Fock theory applied to a realistic model of twisted bilayer graphene, based on the Bistritzer-MacDonald Hamiltonian augmented by screened Coulomb interactions, we find that the twist-tuned quantum phase transition is continuous. We argue that the quantum critical behavior belongs to the relativistic Gross-Neveu-XY universality class, and we characterize it through an effective field theory analysis. Our theoretical predictions can be directly tested using current experimental setups incorporating the recently developed quantum twisting microscope.

cond-mat.mes-hall↗

arXiv2025

Ferrimagnetism from triple-q order in Na$_2$Co$_2$TeO$_6$

The candidate Kitaev magnet Na$_2$Co$_2$TeO$_6$ exhibits a characteristic ferrimagnetic response at low temperatures, with a finite residual magnetization that changes sign at a compensation point located at around half the ordering temperature. We argue that the behavior can be naturally understood to arise in this material as a consequence of a noncollinear triple-$\mathbf{q}$ magnetic ground state. Using large-scale classical Monte Carlo simulations, we study the finite-temperature response of the pertinent honeycomb Heisenberg-Kitaev-$Γ$-$Γ'$ model in weak training fields. Our model features all symmetry-allowed nearest-neighbor exchange interactions, as well as sublattice-dependent next-nearest-neighbor interactions, consistent with the reported crystal structure of the material. We also consider a six-spin ring exchange perturbation, which allows us to tune between the two different magnetic long-range orders that have been suggested for this material in the literature, namely, a collinear single-$\mathbf{q}$ zigzag state and a noncollinear triple-$\mathbf{q}$ state. We demonstrate that the experimentally-observed ferrimagnetic response of Na$_2$Co$_2$TeO$_6$ can be well described within our modeling if the magnetic ground state features noncollinear triple-$\mathbf{q}$ order. The observation of a compensation point, where the residual magnetization reverses sign, suggests a sublattice $g$-factor anisotropy, with a larger out-of-plane $g$-factor on the sublattice with stronger antiferromagnetic intrasublattice exchange. By contrast, a classical Heisenberg-Kitaev-$Γ$-$Γ'$-type model with collinear zigzag ground state is insufficient even in principle to describe the observed behavior. Our results illustrate the unconventional physics of noncollinear magnetic long-range orders hosted by frustrated magnets with bond-dependent interactions.

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arXiv2025

Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets

Pyrochlore magnets have proven to provide an excellent arena for the realization of a variety of many-body phenomena such as classical and quantum order-by-disorder, as well as spin liquid phases described by emergent gauge field theories. These phenomena arise from the competition between different symmetry-breaking magnetic orders. In this work, we consider a subspace of the most general bilinear nearest-neighbor Hamiltonian on the pyrochlore lattice, parameterized by the local interaction parameter $J_{z\pm}$, where three symmetry-breaking phases converge. We demonstrate that for small values of $|J_{z\pm}|$, a conventional $\mathbf q=0$ ordered phase is selected by a thermal order-by-disorder mechanism. For $|J_{z\pm}|$ above a certain finite threshold, a novel spin-nematic phase is stabilized at low temperatures. Instead of the usual Bragg peaks, the spin-nematic phase features lines of high intensity in the spin structure factor. At intermediate temperatures above the low-temperature orders, a rank-2 U(1) classical spin liquid is realized for all $J_{z\pm} \neq 0$. We fully characterize all phases using classical Monte-Carlo simulations and a self-consistent Gaussian approximation.

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arXiv2025

Evolution of entanglement entropy at SU($N$) deconfined quantum critical points

Over the past two decades, the enigma of the deconfined quantum critical point (DQCP) has attracted broad attention across the condensed matter, quantum field theory, and high-energy physics communities, as it is expected to offer a new paradigm in theory, experiment, and numerical simulations that goes beyond the Landau-Ginzburg-Wilson framework of symmetry breaking and phase transitions. However, the nature of DQCP has been controversial. For instance, in the square-lattice spin-1/2 $J$-$Q$ model, believed to realize the DQCP between Néel and valence bond solid states, conflicting results, such as first-order versus continuous transition, and critical exponents incompatible with conformal bootstrap bounds, have been reported. The enigma of DQCP is exemplified in its anomalous logarithmic subleading contribution in its entanglement entropy (EE), which was discussed in recent studies. In the current work, we demonstrate that similar anomalous logarithmic behavior persists in a class of models analogous to the DQCP. We systematically study the quantum EE of square-lattice SU($N$) DQCP spin models. Based on large-scale quantum Monte Carlo computation of the EE, we show that for a series of $N$ smaller than a critical value, the anomalous logarithmic behavior always exists in the EE, which implies that the previously determined DQCPs in these models do not belong to conformal fixed points. In contrast, when $N\ge N_c$ with a finite $N_c$ that we evaluate to lie between $7$ and $8$, the DQCPs are consistent with conformal fixed points that can be understood within the Abelian Higgs field theory with $N$ complex components.

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arXiv2024

Critical properties of metallic and deconfined quantum phase transitions in Dirac systems

We characterize, by means of large-scale fermion quantum Monte Carlo simulations, metallic and deconfined quantum phase transitions in a bilayer honeycomb model in terms of their quantum critical and finite-temperature properties.The model features three different phases at zero temperature as function of interaction strength. At weak interaction, a fully symmetric Dirac semimetal state is realized. At intermediate and strong interaction, respectively, two long-range-ordered phases that break different symmetries are stabilized. The ordered phases feature partial and full, respectively, gap openings in the fermion spectrum. The first transition between the disordered and long-range-ordered semimetallic phases has previously been argued to be described by the $(2+1)$-dimensional Gross-Neveu-SO(3) field theory. By performing simulations with an improved symmetric Trotter decomposition, we further substantiate this claim by computing the critical exponents $1/ν$, $η_ϕ$, and $η_ψ$, which turn out to be consistent with the field-theoretical expectation within numerical and analytical uncertainties. The second transition between the two long-range-ordered phases has previously been proposed as a possible instance of a metallic deconfined quantum critical point. We further develop this scenario by analyzing the spectral functions in the single-particle, particle-hole, and particle-particle channels. Our results indicate gapless excitations with a unique velocity, supporting the emergence of Lorentz symmetry at criticality. We also compute the finite-temperature phase boundaries of the ordered states above the fully gapped state at large interaction. The phase boundaries vanishes smoothly in the vicinity of the putative metallic deconfined quantum critical point, in agreement with the expectation for a continuous or weakly-first-order transition.

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arXiv2024

Quasiuniversality from all-in-all-out Weyl quantum criticality in pyrochlore iridates

We identify an exotic quasiuniversal behavior near the all-in-all-out Weyl quantum critical point in three-dimensional Luttinger semimetals, such as the pyrochlore iridates $R_2$Ir$_2$O$_7$, with $R$ a rare-earth element. The quasiuniversal behavior is characterized by power laws with exponents that vary slowly over several orders of magnitude in energy or length. However, in contrast to the quasiuniversality discussed in the context of deconfined criticality, the present case is characterized by a genuinely-universal ultra-low-temperature behavior. In this limit, the pertinent critical exponents can be computed exactly within a renormalization group analysis. Experimental implications for the pyrochlore iridates are outlined.

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arXiv2024

Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na$_2$Co$_2$TeO$_6$

The honeycomb magnet Na$_2$Co$_2$TeO$_6$ has recently been argued to realize an approximate hidden SU(2) symmetry that can be understood by means of a duality transformation. Using large-scale classical Monte Carlo simulations, we study the finite-temperature phase diagram of the pertinent Heisenberg-Kitaev-$Γ$-$Γ'$ model near the hidden-SU(2)-symmetric point, in the presence of a six-spin ring exchange perturbation. At low temperatures, the model features collinear single-$\mathbf{q}$ zigzag and noncollinear triple-$\mathbf{q}$ ground states, depending on the sign of the ring exchange coupling. We show that in the vicinity of the hidden-SU(2)-symmetric point, the magnetic long-range orders melt in two stages. The corresponding finite-temperature transitions are continuous and fall into 2D Ising and 2D Potts universality classes, respectively. The two fluctuation-induced phases at intermediate temperatures spontaneously break spin rotational and lattice translational symmetries, respectively, but both leave time reversal symmetry intact. They are characterized by finite expectation values of a real, symmetric, traceless, second-rank tensor, and are naturally understood as vestigial orders of the underlying magnetic states. We identify these vestigial orders as $\mathbb{Z}_3$ spin nematic and $\mathbb{Z}_4$ spin current density wave phases, respectively. For increasing ring exchange perturbations, the width of the vestigial phases decreases, eventually giving rise to a direct first-order transition from the magnetically-ordered phase to the disordered paramagnet. We propose the $\mathbb{Z}_4$ spin current density wave phase, which is the vestigial phase of the primary triple-$\mathbf q$ magnetic order, as a natural candidate for the paramagnetic 2D long-range-ordered state observed in Na$_2$Co$_2$TeO$_6$ in a small window above the antiferromagnetic ordering temperature.

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