arXiv subjects

Joseph Maciejko

Publications and source records attributed to Joseph Maciejko.

At least 37 records · Page 2Linked to original sources

arXiv2022

Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice

In a first-order topological phase with sublattice degrees of freedom, a change in the boundary sublattice termination has no effect on the existence of gapless boundary states in dimensions higher than one. However, such a change may strongly affect the physical properties of those boundary states. Motivated by this observation, we perform a systematic study of the impact of sublattice terminations on the boundary physics on the two-dimensional kagome lattice. We find that the energies of the Dirac points of helical edge states in two-dimensional first-order topological kagome insulators sensitively depend on the terminating sublattices at the edge. Remarkably, this property admits the realization of a time-reversal invariant second-order topological superconducting phase with highly controllable Majorana Kramers pairs at the corners and sublattice domain walls by putting the topological kagome insulator in proximity to a $d$-wave superconductor. Moreover, substituting the $d$-wave superconductor with a conventional $s$-wave superconductor, we find that highly controllable Majorana zero modes can also be realized at the corners and sublattice domain walls if an in-plane Zeeman field is additionally applied. Our study reveals promising platforms to implement highly controllable Majorana zero modes.

cond-mat.supr-con↗

arXiv2022

Quantum-critical electrodynamics of Luttinger fermions

We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative $U(1)$ quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations, and can thus also be viewed as a $U(1)$ spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.

cond-mat.str-el↗

arXiv2022

Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study

We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with $N=2$ spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength $U_c = 7.28 \pm 0.02$ in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding $N=2$ chiral Ising Gross-Neveu universality class: the inverse correlation length exponent $ν^{-1} = 1.19 \pm 0.03$, the order parameter anomalous dimension $η_ϕ = 0.31 \pm 0.01$, and the fermion anomalous dimension $η_ψ = 0.136 \pm 0.005$.

cond-mat.str-el↗

arXiv2022

Automorphic Bloch theorems for hyperbolic lattices

Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle eigenstates and eigenenergies for hopping on such a lattice, a hyperbolic generalization of band theory was previously constructed, based on ideas from algebraic geometry. In this hyperbolic band theory, eigenstates are automorphic functions, and the Brillouin zone is a higher-dimensional torus, the Jacobian of the compactified unit cell understood as a higher-genus Riemann surface. Three important questions were left unanswered: whether a band theory can be expected to hold for a non-Euclidean lattice, where translations do not generally commute; whether a formal Bloch theorem can be rigorously established; and whether hyperbolic band theory can describe finite lattices realized in experiment. In the present work, we address all three questions simultaneously. By formulating periodic boundary conditions for finite but arbitrarily large lattices, we show that a generalized Bloch theorem can be rigorously proved, but may or may not involve higher-dimensional irreducible representations (irreps) of the nonabelian translation group, depending on the lattice geometry. Higher-dimensional irreps corrrespond to points in a moduli space of higher-rank stable holomorphic vector bundles, which further generalizes the notion of Brillouin zone beyond the Jacobian. For a large class of finite lattices, only 1D irreps appear, and the hyperbolic band theory previously developed becomes exact.

cond-mat.mes-hall↗

arXiv2022

Crystallography of Hyperbolic Lattices

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive, for the first time, a list of example hyperbolic $\{p,q\}$ lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians. Our work lays the foundation for generalizing some of the most powerful concepts of solid state physics, crystal momentum and Brillouin zone, to the emerging field of hyperbolic lattices and tabletop simulations of gravitational theories, and reveals the connections to concepts from topology and algebraic geometry.

cond-mat.str-el↗

arXiv2022

Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals

In the presence of certain symmetries, three-dimensional Dirac semimetals can harbor not only surface Fermi arcs, but also surface Dirac cones. Motivated by the experimental observation of rotation-symmetry-protected Dirac semimetal states in iron-based superconductors, we investigate the potential intrinsic topological phases in a $C_{4z}$-rotational invariant superconducting Dirac semimetal with $s_{\pm}$-wave pairing. When the normal state harbors only surface Fermi arcs on the side surfaces, we find that an interesting gapped superconducting state with a quartet of Bogoliubov-Dirac cones on each side surface can be realized, even though the first-order topology of its bulk is trivial. When the normal state simultaneously harbors surface Fermi arcs and surface Dirac cones, we find that a second-order time-reversal invariant topological superconductor with helical Majorana hinge states can be realized. The criteria for these two distinct topological phases have a simple geometric interpretation in terms of three characteristic surfaces in momentum space. By reducing the bulk material to a thin film normal to the axis of rotation symmetry, we further find that a two-dimensional first-order time-reversal invariant topological superconductor can be realized if the inversion symmetry is broken by applying a gate voltage. Our work reveals that diverse topological superconducting phases and types of Majorana modes can be realized in superconducting Dirac semimetals.

cond-mat.supr-con↗

arXiv2022

Triangular pair density wave in confined superfluid $^3$He

Recent advances in experiment and theory suggest that superfluid $^3$He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.

cond-mat.supr-con↗

arXiv2021

Hyperbolic band theory

The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit quantum electrodynamics, we exploit ideas from algebraic geometry to construct the first hyperbolic generalization of Bloch theory, despite the absence of commutative translation symmetries. For a quantum particle propagating in a hyperbolic lattice potential, we construct a continuous family of eigenstates that acquire Bloch-like phase factors under a discrete but noncommutative group of hyperbolic translations, the Fuchsian group of the lattice. A hyperbolic analog of crystal momentum arises as the set of Aharonov-Bohm phases threading the cycles of a higher-genus Riemann surface associated with this group. This crystal momentum lives in a higher-dimensional Brillouin zone torus, the Jacobian of the Riemann surface, over which a discrete set of continuous energy bands can be computed.

cond-mat.mes-hall↗

arXiv2021

LaN Structural and Topological Transitions Driven by Temperature and Pressure

We study lanthanum mononitride LaN by first-principles calculations. The commonly reported rock-salt structure of $Fm\bar{3}m$ symmetry for rare-earth monopnictides is found dynamically unstable for LaN at zero temperature. Using density functional theory and evolutionary crystal prediction, we discover a new, dynamically stable structure with $P1$ symmetry at 0 K. This $P1$-LaN exhibits spontaneous electric polarization. Our ab initio molecular dynamics simulations of finite-temperature phonon spectra further suggest that LaN will undergo ferroelectric and structural transitions from $P1$ to $Fm\bar{3}m$ symmetry, when temperature is increased. Moreover, $P1$-LaN will transform to a tetragonal structure with $P4/nmm$ symmetry at a critical pressure $P=18$ GPa at 0 K. Electronic structures computed with an advanced hybrid functional show that the high-temperature rock-salt LaN can change from a trivial insulator to a strong topological insulator at $P \sim 14$ GPa. Together, our results indicate that when $P=14 - 18$ GPa, LaN can show simultaneous temperature-induced structural, ferroelectric, and topological transitions. Lanthanum monopnictides thereby provide a rich playground for exploring novel phases and phase transitions driven by temperature and pressure.

cond-mat.mtrl-sci↗

arXiv2021

Symmetry-breaking effects of instantons in parton gauge theories

Compact quantum electrodynamics (CQED$_3$) with Dirac fermionic matter provides an adequate framework for elucidating the universal low-energy physics of a wide variety of (2+1)D strongly correlated systems. Fractionalized states of matter correspond to its deconfined phases, where the gauge field is effectively noncompact, while conventional broken-symmetry phases are associated with confinement triggered by the proliferation of monopole-instantons. While much attention has been devoted lately to the symmetry classification of monopole operators in massless CQED$_3$ and related 3D conformal field theories, explicit derivations of instanton dynamics in parton gauge theories with fermions have been lacking. In this work, we use semiclassical methods analogous to those used by 't Hooft in the solution of the $U(1)$ problem in 4D quantum chromodynamics (QCD) to explicitly demonstrate the symmetry-breaking effect of instantons in CQED$_3$ with massive fermions, motivated by a fermionic parton description of hard-core bosons on a lattice. By contrast with the massless case studied by Marston, we find that massive fermions possess Euclidean zero modes exponentially localized to the center of the instanton. Such Euclidean zero modes produce in turn an effective four-fermion interaction -- known as the 't Hooft vertex in QCD -- which naturally leads to two possible superfluid phases for the original microscopic bosons: a conventional single-particle condensate or an exotic boson pair condensate without single-particle condensation.

cond-mat.str-el↗

arXiv2021

Quantum phase transitions in Dirac fermion systems

A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.

cond-mat.str-el↗

arXiv2021

Critical exponents for the valence-bond-solid transition in lattice quantum electrodynamics

Recent sign-problem-free quantum Monte Carlo simulations of (2+1)-dimensional lattice quantum electrodynamics (QED$_3$) with $N_f$ flavors of fermions on the square lattice have found evidence of continuous quantum phase transitions between a critical phase and a gapped valence-bond-solid (VBS) phase for flavor numbers $N_f=4$, $6$, and $8$. We derive the critical theory for these transitions, the chiral $O(2)$ QED$_3$-Gross-Neveu model, and show that the latter is equivalent to the gauged Nambu--Jona-Lasinio model. Using known large-$N_f$ results for the latter, we estimate the order parameter anomalous dimension and the correlation length exponent for the transitions mentioned above. We obtain large-$N_f$ results for the dimensions of fermion bilinear operators, in both the gauged and ungauged chiral $O(2)$ Gross-Neveu models, which respectively describe the long-distance power-law decay of two-particle correlation functions at the VBS transition in lattice QED$_3$ and the Kekulé-VBS transition for correlated fermions on the honeycomb lattice.

cond-mat.str-el↗

arXiv2020

Random-mass disorder in the critical Gross-Neveu-Yukawa models

An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario---continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length---as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance.

cond-mat.str-el↗

arXiv2020

Antiferromagnetic transitions of Dirac fermions in three dimensions

We use determinant quantum Monte Carlo (DQMC) simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $π$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-ranged AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)d Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in birefringent Dirac fermion system. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions, and may be observed using ultracold atoms in an optical lattice.

cond-mat.str-el↗

arXiv2020

Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number $N_f$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED$_3$) on the square lattice have found evidence for a continuous quantum phase transition between a power-law correlated conformal QED$_3$ phase and a confining valence-bond-solid phase with spontaneously broken point-group symmetries. The critical continuum theory of this transition was shown to be the $O(2)$ QED$_3$-Gross-Neveu model, equivalent to the gauged Nambu-Jona-Lasinio model, and critical exponents were computed to first order in the large-$N_f$ expansion and the $ε$ expansion. We extend these studies by computing critical exponents to second order in the large-$N_f$ expansion and to four-loop order in the $ε$ expansion below four spacetime dimensions. In the latter context, we also explicitly demonstrate that the discrete $\mathbb{Z}_4$ symmetry of the valence-bond-solid order parameter is dynamically enlarged to a continuous $O(2)$ symmetry at criticality for all values of $N_f$.

cond-mat.str-el↗

arXiv2019

Critical properties of the Néel/algebraic-spin-liquid transition

The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $π$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy Néel order and drive a direct quantum phase transition to the $π$-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED$_3$-Gross-Neveu-Yukawa model with a single SU(2) doublet of four-component Dirac fermions (i.e., $N_f=1$), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $ε$ expansion below four spacetime dimensions to four-loop order, and a large-$N_f$ expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-Néel transition for interacting fermions on the honeycomb lattice.

cond-mat.str-el↗

arXiv2019

Exactly solvable Majorana-Anderson impurity models

Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the $\mathbb{Z}_2$ slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. For a spin-polarized Kitaev chain coupled to a quantum dot, we obtain exact expressions for the dot spectral functions at both zero and finite temperature. We study how the interaction strength and localization length of the end Majorana zero mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations, as well as the local electronic density of states in the superconducting chain.

cond-mat.str-el↗

arXiv2019

Deconfined criticality in the QED$_{3}$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited

The critical properties of the QED$_{3}$ Gross-Neveu-Yukawa (GNY) model in 2+1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the Néel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $ε$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the QED$_{3}$ GNY critical point are in reasonable agreement with numerical studies of the Néel-to-VBS transition, in support of the duality conjecture.

cond-mat.str-el↗