arXiv subjects

Stefan Wessel

Publications and source records attributed to Stefan Wessel.

At least 37 records · Page 2Linked to original sources

arXiv2022

Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C$_9$H$_{18}$N$_2$CuBr$_4$. Single-crystal heat capacity and neutron diffraction measurements reveal that the N$\rm \acute{e}$el-ordered phase breaks down beyond a critical pressure of $P_{\rm c}$$\sim$1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above $P_{\rm c}$.

cond-mat.str-el↗

arXiv2022

Cluster quantum Monte Carlo study of two-dimensional weakly-coupled frustrated trimer antiferromagnets

We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La${}_4$Cu${}_3$MoO${}_{12}$. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down to the low-temperature regime. Besides exploring the thermodynamic behavior for the triangle-square lattice model we also assess a mean field theory-based prediction for the onset of chiral order. For the breathing distorted kagome lattice model, we observe a robust two-peak structure in the specific heat, both in the quantum spin liquid and the lattice-nematic regimes.

cond-mat.str-el↗

arXiv2022

Hierarchical single-ion anisotropies in spin-1 Heisenberg antiferromagnets on the honeycomb lattice

We examine the thermal properties of the spin-1 Heisenberg antiferromagnet on the honeycomb lattice in the presence of an easy-plane single-ion anisotropy as well as the effects of an additional weak in-plane easy-axis anisotropy. In particular, using large-scale quantum Monte Carlo simulations, we analyze the scaling of the correlation length near the thermal phase transition into the ordered phase. This allows us to quantify the temperature regime above the critical point in which -- in spite of the additional in-plane easy-axis anisotropy -- characteristic easy-plane physics, such as near a Berezinskii-Kosterlitz-Thouless transition, can still be accessed. Our theoretical analysis is motivated by recent neutron scattering studies of the spin-1 compound BaNi${}_2$V${}_2$O${}_8$ in particular, and it addresses basic quantum spin models for generic spin-1 systems with weak anisotropies, which we probe over the full range of experimentally relevant correlation length scales.

cond-mat.str-el↗

arXiv2022

Surrogate models for quantum spin systems based on reduced order modeling

We present a methodology to investigate phase-diagrams of quantum models based on the principle of the reduced basis method (RBM). The RBM is built from a few ground-state snapshots, i.e., lowest eigenvectors of the full system Hamiltonian computed at well-chosen points in the parameter space of interest. We put forward a greedy-strategy to assemble such small-dimensional basis, i.e., to select where to spend the numerical effort needed for the snapshots. Once the RBM is assembled, physical observables required for mapping out the phase-diagram (e.g., structure factors) can be computed for any parameter value with a modest computational complexity, considerably lower than the one associated to the underlying Hilbert space dimension. We benchmark the method in two test cases, a chain of excited Rydberg atoms and a geometrically frustrated antiferromagnetic two-dimensional lattice model, and illustrate the accuracy of the approach. In particular, we find that the ground-manifold can be approximated to sufficient accuracy with a moderate number of basis functions, which increases very mildly when the number of microscopic constituents grows - in stark contrast to the exponential growth of the Hilbert space needed to describe each of the few snapshots. A combination of the presented RBM approach with other numerical techniques circumventing even the latter big cost, e.g., Tensor Network methods, is a tantalising outlook of this work.

quant-ph↗

arXiv2021

Quantum Monte Carlo simulations of highly frustrated magnets in a cluster basis: The two-dimensional Shastry-Sutherland model

Quantum Monte Carlo (QMC) simulations constitute nowadays one of the most powerful methods to study strongly correlated quantum systems, provided that no "sign problem" arises. However, many systems of interest, including highly frustrated magnets, suffer from an average sign that is close to zero in standard QMC simulations. Nevertheless, a possible sign problem depends on the simulation basis, and here we demonstrate how a suitable choice of cluster basis can be used to eliminate or at least reduce the sign problem in highly frustrated magnets that were so far inaccessible to efficient QMC simulations. We focus in particular on the application of a two-spin (dimer)-based QMC method to the thermodynamics of the spin-1/2 Shastry-Sutherland model for SrCu$_2$(BO$_3$)$_2$.

cond-mat.str-el↗

arXiv2021

Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations

Analytic predictions have been derived recently by V. Dohm and S. Wessel, Phys. Rev. Lett. {\bf 126}, 060601 (2021) from anisotropic $φ^4$ theory and conformal field theory for the amplitude ${\cal F}_c$ of the critical free energy of finite anisotropic systems in the two-dimensional Ising universality class. These predictions employ the hypothesis of multiparameter universality. We test these predictions by means of high-precision Monte Carlo (MC) simulations for ${\cal F}_c$ of the Ising model on a square lattice with isotropic ferromagnetic couplings between nearest neighbors and with an anisotropic coupling between next-nearest neighbors along one diagonal. We find remarkable agreement between the MC data and the analytical prediction. This agreement supports the validity of multiparameter universality and invalidates two-scale-factor universality as ${\cal F}_c$ is found to exhibit a nonuniversal dependence on the microscopic couplings of the scalar $φ^4$ model and the Ising model. Our results are compared with the exact result for ${\cal F}_c$ in the three-dimensional $φ^4$ model with a planar anisotropy in the spherical limit. The critical Casimir amplitude is briefly discussed.

cond-mat.stat-mech↗

arXiv2021

Global hierarchy vs. local structure: spurious self-feedback in scale-free networks

Networks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to be key to the collective network behavior, e.g., in Ising models on such complex topologies. This applies in particular to the transition into a globally ordered network state, which thereby proceeds in a hierarchical fashion, and with a non-trivial local structure. Standard mean-field theory of Ising models on scale-free networks underrates the presence of the hubs, while nevertheless providing remarkably reliable estimates for the onset of global order. Here, we expose that a spurious self-feedback effect, inherent to mean-field theory, underlies this apparent paradox. More specifically, we demonstrate that higher order interaction effects precisely cancel the self-feedback on the hubs, and we expose the importance of hubs for the distinct onset of local versus global order in the network. Due to the generic nature of our arguments, we expect the mechanism that we uncover for the archetypal case of Ising networks of the Barabási-Albert type to be also relevant for other systems with a strongly hierarchical underlying network structure.

cond-mat.dis-nn↗

arXiv2021

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with ${n_\text{D}=4}$ component Dirac spinors in $D=(2+1)$ dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or $π$-flux square lattice. The torus energy spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here, we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical torus energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus energy spectrum analytically using the perturbative expansion in ${ε= 4 - D}$, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical torus energy spectrum and we observe prominent multiplicity features related to an emergent symmetry predicted from the quantum field theory. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.

cond-mat.str-el↗

arXiv2021

Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in $d\geq 2$ Dimensions

The exact critical Casimir amplitude is derived for anisotropic systems within the $d=2$ Ising universality class by combining conformal field theory (CFT) with anisotropic $φ^4$ theory. Explicit results are presented for the general anisotropic scalar $φ^4$ model and for the fully anisotropic triangular-lattice Ising model in finite rectangular and infinite strip geometries with periodic boundary conditions (PBC). These results demonstrate the validity of multiparameter universality for confined anisotropic systems and the nonuniversality of the critical Casimir amplitude. We find an unexpected complex form of self-similarity of the anisotropy effects near the instability where weak anisotropy breaks down. This can be traced back to the property of modular invariance of isotropic CFT for $d=2$. More generally, for $d>2$ we predict the existence of self-similar structures of the finite-size scaling functions of $O(n)$-symmetric systems with planar anisotropies and PBC both in the critical region for $ n \geq 1$ as well as in the Goldstone-dominated low-temperature region for $ n \geq 2$.

cond-mat.stat-mech↗

arXiv2020

Spin vs. bond correlations along dangling edges of quantum critical magnets

Dangling edge spins of two-dimensional quantum critical antiferromagnets display strongly enhanced spin correlations with scaling dimensions that fall outside of the classical theory of surface critical phenomena. We provide large-scale quantum Monte Carlo results for both spin and bond correlation functions for the case of the columnar dimer model in particular. Unlike the spin correlations, we find the bond correlations to differ starkly between the spin-1/2 and spin-1 case. Furthermore, we compare the corresponding scaling dimensions to recent theoretical predictions. These predictions are, in part, supported by our numerical data, but cannot explain our findings completely. Our results thus put further constraints on completing the understanding of dangling edge correlations, as well as surface phenomena in strongly-correlated quantum systems in general.

cond-mat.str-el↗

arXiv2020

Reduction of the sign problem near $T=0$ in quantum Monte Carlo simulations

Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero temperature limit in frustrated quantum spin models. If the Hamiltonian of interest and the sign-problem-free Hamiltonian---obtained by making all off-diagonal elements negative in a given basis---have the same ground state and this state is a member of the computational basis, then the average sign returns to one as the temperature goes to zero. We illustrate this technique by studying the triangular and kagome lattice Heisenberg antiferrromagnet in a magnetic field above saturation, as well as the Heisenberg antiferromagnet on a modified Husimi cactus in the dimer basis. We also provide detailed appendices on using linear programming techniques to automatically generate efficient directed loop updates in quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2020

Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation

The magnetic properties of graphene on finite geometries are studied using a self-consistent mean-field theory of the Hubbard model. This approach is known to predict ferromagnetic edge states close to the zig-zag edges in single-layer graphene quantum dots and nanoribbons. In order to assess the accuracy of this method, we perform complementary exact diagonalization and quantum Monte Carlo simulations. We observe good quantitative agreement for all quantities investigated provided that the Coulomb interaction is not too strong.

cond-mat.str-el↗

arXiv2020

Quantifying the fragility of unprotected quadratic band crossing points

We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on the honeycomb lattice with nearest neighbor hopping $t$ and third-nearest neighbor hopping $t''$, which exhibits fine-tuned QBCPs at the corners of the Brillouin zone for ${t'' = t/2}$. In this situation, the density of states remains finite at the Fermi level of the half-filled band and repulsive nearest-neighbor interactions $V$ lead to a charge-density-wave (CDW) instability at infinitesimally small $V$ in the random-phase approximation or mean-field theory. We examine the fragility of the QBCPs against dispersion renormalizations in the ${t\mbox{-}t''\mbox{-}V}$ model using perturbation theory, and find that the $t''$-value needed for the QBCPs increases with $V$ due to the hopping renormalization. However, the instability toward CDW formation always requires a nonzero threshold interaction strength, i.e., one cannot fine-tune $t''$ to recover the QBCPs in the interacting system. These perturbative arguments are supported by quantum Monte Carlo simulations for which we carefully compare the corresponding threshold scales at and beyond the QBCP fine-tuning point. From this analysis, we thus gain a quantitative microscopic understanding of the fragility of the QBCPs in this basic interacting fermion system.

cond-mat.str-el↗

arXiv2019

Comment on "The role of electron-electron interactions in two-dimensional Dirac fermions''

Tang et al. [Science 361, 570 (2018)] report on the properties of Dirac fermions with both on-site and Coulomb interactions. The substantial decrease up to ~40% of the Fermi velocity of Dirac fermions with on-site interaction is inconsistent with the numerical data near the Gross-Neveu quantum critical point. This results from an inappropriate finite-size extrapolation.

cond-mat.str-el↗

arXiv2019

Emergent symmetries and coexisting orders in Dirac fermion systems

The quantum phase diagram and critical behavior of two-dimensional Dirac fermions coupled to two compatible order-parameter fields with $O(N_1)\oplus O(N_2)$ symmetry is investigated. Recent numerical studies of such systems have reported evidence for non-Landau-Ginzburg-Wilson transitions and emergent $O(N_1+N_2)$ symmetry between the two ordered states, which has been interpreted within a scenario of deconfined quantum criticality in (2+1)-dimensional Dirac materials. Here, we provide two theoretical approaches to refine the phase diagrams of such systems. In the immediate vicinity of the multicritical point between the ordered phases and the semimetallic phase, we employ a non-perturbative field-theoretical analysis based on the functional renormalization group. For the particular case of $N_1=3$, $N_2=1$, we perform a large-scale quantum Monte Carlo analysis of the strong-coupling region, where both orders meet. Our findings support the robust emergence of enhanced symmetry at the multicritical point and suggest the transition between the two ordered phases to take place via a sequence of continuous transitions. In particular, we find that intermediate regimes of coexistence are present in the phase diagram for all values of $N_1$ and $N_2$.

cond-mat.str-el↗

arXiv2019

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

The thermodynamic properties of the Shastry-Sutherland model have posed one of the longest-lasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat around the QPT, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

cond-mat.str-el↗

arXiv2019

Spin dynamics of the planar kagome lattice ferromagnet with four-site ring exchange processes

By means of quantum Monte Carlo simulations, combined with a stochastic analytic continuation, we examine the spin dynamics of the spin-1/2 planar (XY) ferromagnet on the kagome lattice with additional four-site ring exchange terms. Such exchange processes were previously considered to lead into an extended $Z_2$ quantum spin liquid phase beyond a quantum critical point from the XY-ferromagnet. We examine the dynamical spin structure factor in the non-magnetic regime and probe for signatures of spin fractionalization. Furthermore, we contrast our findings and the corresponding energy scales of the excitation gaps in the ring exchange model to those emerging in a related Balents-Fisher-Girvin model with a $Z_2$ quantum spin liquid phase, and monitor the softening of the magnon mode upon approaching the quantum critical point from the XY-ferromagnetic regime.

cond-mat.str-el↗

arXiv2019

Nonordinary criticality at the edges of planar spin-1 Heisenberg antiferromagnets

Dangling edge spins of dimerized two-dimensional spin-1 Heisenberg antiferromagnets are shown to exhibit nonordinary quantum critical correlations, akin to the scaling behavior observed in recently explored spin-1/2 systems. Based on large-scale quantum Monte Carlo simulations, we observe remarkable similarities between these two cases, and also examine the crossover to the fundamentally distinct behavior in the one-dimensional limit of strongly coupled edge spins. We complement our numerical analysis by a cluster mean-field theory that encompasses the qualitatively similar behavior for the spin-1 and the spin-1/2 case, and its dependence on the spatial edge spin configuration in a generic way.

cond-mat.str-el↗