Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations

Abstract

We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo methods but which still host complex many-body states and quantum phase transitions of interest in condensed matter physics. We focus on quantum spin systems in which competing interactions lead to non-magnetic ground states. These states and the associated quantum phase transitions can be studied in great detail, enabling direct access to universal properties and connections with low-energy effective quantum field theories. As specific examples, we discuss the transition from a Neel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetry-broken valence-bond solid in SU(2) and SU(N) invariant spin models. We also discuss anisotropic (XXZ) systems harboring topological Z2 spin liquids and the XY* transition. We briefly review recent progress on quantum Monte Carlo algorithms, including ground state projection in the valence-bond basis and direct computation of the Renyi variants of the entanglement entropy.

23 pages, 10 figures

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• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
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• Deconfined quantum criticality and Neel order via dimer disorder
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• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Phase diagram of depleted Heisenberg model for CaV4O9
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• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
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• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• Schwinger Boson Mean Field Theories of Spin Liquid States on Honeycomb Lattice: Projective Symmetry Group Analysis and Critical Field Theory
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Striped phase in a quantum XY-model with ring exchange
• Phase diagram of the disordered Bose-Hubbard model
• Magnetic Excitations in the Spin-1 Anisotropic Heisenberg Antiferromagnetic Chain System NiCl${}_2$-4SC(NH${}_2$)${}_2$
• Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Ground state projection of quantum spin systems in the valence bond basis
• Accessing the dynamics of large many-particle systems using Stochastic Series Expansion
• D-wave correlated Critical Bose Liquids in two dimensions
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• Universal nonequilibrium quantum dynamics in imaginary time
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• The fermion bag approach to lattice field theories
• Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
• Detecting Quantum Critical Points using Bipartite Fluctuations
• Microscopic models for fractionalized phases in strongly correlated systems
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Infinite-randomness quantum critical points induced by dissipation
• Universal Signatures of Fractionalized Quantum Critical Points
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model
• The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
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• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Some formal results for the valence bond basis
• Theory of smeared quantum phase transitions
• Superfluid-insulator transition of disordered bosons in one-dimension
• Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy
• Universal scaling at field-induced magnetic phase transitions
• Nearly critical ground state of LaCuO2.5
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• 3D loop models and the CP^{n-1} sigma model
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Impurity spin texture at a deconfined quantum critical point
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Monopoles in CP(N-1) model via the state-operator correspondence
• The plaquette phase of the square lattice quantum dimer model
• Quantum Transition between an Antiferromagnetic Mott Insulator and $d_{x^2-y^2}$ Superconductor in Two Dimensions
• Quantum-Critical Behavior in a Two-Layer Antiferromagnet
• Quantum criticality in SU(3) and SU(4) anti-ferromagnets
• Vanishing of the negative-sign problem of quantum Monte Carlo simulations in one-dimensional frustrated spin systems
• Percolation quantum phase transitions in diluted magnets
• Mott glass in site-diluted S=1 antiferromagnets with single-ion anisotropy
• Ground States of the SU(N) Heisenberg Model
• Spin Supersolid in Anisotropic Spin-One Heisenberg Chain
• Criticality in Trapped Atomic Systems
• A Mott Glass to Superfluid Transition for Random Bosons in Two Dimensions
• Two-particle decay and quantum criticality in dimerized antiferromagnets
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Two-dimensional quantum antiferromagnets
• Spin liquid ground state in a two dimensional non-frustrated spin model
• Method to characterize spinons as emergent elementary particles
• Dimer-Quadrupolar Quantum Phase Transition in the Quasi-One-Dimensional Heisenberg Model with Biquadratic Interaction
• Reading entanglement in terms of spin configurations in quantum magnets
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• Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
• Impurity induced spin texture in quantum critical 2D antiferromagnets
• Example of a first-order Néel to Valence-Bond-Solid transition in two-dimensions
• Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange
• Critical structure factors of bilinear fields in O(N)-vector models
• Quantum Critical Dynamics Simulation of Dirty Boson Systems
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• Quantum-criticality and percolation in dimer-diluted 2D antiferromagnets
• Impurity effects at finite temperature in the two-dimensional S=1/2 Heisenberg antiferromagnet
• Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
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• Large-N estimates of universal amplitudes of the CP^{N-1} theory and comparison with the JQ model
• Thermodynamics of a gas of deconfined bosonic spinons in two dimensions
• Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets
• Vacancy-induced spin texture in a one dimensional $S=1/2$ Heisenberg antiferromagnet
• Quantum spin liquid in a kagome lattice spin-1/2 XY model with four-site exchange
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets
• Exotic phase diagram of a cluster charging model of bosons on the kagome lattice
• Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion
• Imaging bond order near non-magnetic impurities in square lattice antiferromagnets
• Knight shifts around vacancies in the 2D Heisenberg model
• Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets
• Impurity-induced frustration in correlated oxides
• Universal Neel Temperature in Three-Dimensional Quantum Antiferromagnets
• Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
• Neel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model
• A Superglass Phase of Interacting Bosons
• Finite temperature properties of the two-dimensional SU(2) Kondo-necklace
• Universal Finite Temperature Properties of a Three Dimensional Quantum Antiferromagnet in the Vicinity of a Quantum Critical Point
• Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems
• Correlated valence-bond states
• Deconfined quantum criticality and logarithmic violations of scaling from emergent gauge symmetry
• Universal Scaling of the Neel Temperature of Near-Quantum-Critical Quasi-Two-Dimensional Heisenberg Antiferromagnets
• Tuning the disorder of superglasses

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• Machine learning quantum phases of matter beyond the fermion sign problem
• Provably efficient machine learning for quantum many-body problems
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Fate of CP(N-1) fixed points with q-monopoles
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Coherent and dissipative dynamics at quantum phase transitions
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Entanglement negativity via replica trick: a Quantum Monte Carlo approach
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Global symmetries, volume independence and continuity
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Entanglement entropy from nonequilibrium work
• Emmy Noether looks at the deconfined quantum critical point
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Reconstructing the quantum critical fan of strongly correlated systems via quantum correlations
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets
• Spin nematics, valence-bond solids and spin liquids in SO($N$) quantum spin models on the triangular lattice
• Phase transitions in 3D loop models and the $C{P}^{n-1}$ $\sigma$ model
• Antiferromagnetism induced by electron-phonon-coupling
• Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice
• Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Consistent scaling exponents at the deconfined quantum-critical point
• Edge quantum criticality and emergent supersymmetry in topological phases
• Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d
• Entanglement guided search for parent Hamiltonians
• Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Velocity of excitations in ordered, disordered and critical antiferromagnets
• Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Length Distributions in Loop Soups
• Conserved current correlators of conformal field theories in 2+1 dimensions
• Spin nematic ground state of the triangular lattice S=1 biquadratic model
• Wavefunction positivization via automatic differentiation
• Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets
• Stochastic series expansion simulation of the $t$-$V$ model
• Microscopic theory of non-adiabatic response in real and imaginary time
• New easy-plane ${\mathbb{CP}}^{N-1}$ fixed points
• Measuring von Neumann entanglement entropies without wave functions
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Landau ordering phase transitions beyond the Landau paradigm
• Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
• Intrinsic transverse field in frustrated quantum Ising magnets: its physical origin and quantum effects
• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• First-order superfluid to valence bond solid phase transitions in easy-plane SU($N$) magnets for small-$N$
• Sign Problem in Quantum Monte Carlo Simulation
• Thermal valence-bond-solid transition of quantum spins in two dimensions
• Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians
• Quantum-critical scaling properties of the two-dimensional random-singlet state
• Stress tensor and current correlators of interacting conformal field theories in 2+1 dimensions: Fermionic Dirac matter coupled to U(1) gauge field
• Field-driven quantum phase transitions in $S=1/2$ spin chains
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin Liquids
• Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model
• Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
• First order phase transitions in the square lattice "easy-plane" J-Q model
• First-order Néel-cVBS transition in a model square lattice $S=1$ antiferromagnet
• Destroying a topological quantum bit by condensing Ising vortices
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• 1D valence bond solids in a magnetic field
• Lanczos steps to improve variational wave functions
• Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Recent progress on cluster and meron algorithms for strongly correlated systems
• Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
• Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets
• Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point
• Thermal critical points from competing singlet formations in fully frustrated bilayer antiferromagnets
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Topological physics in quantum critical systems
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
• The Future of the Correlated Electron Problem
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Metals get an awkward cousin
• Geometric and computational aspects of chiral topological quantum matter
• Pseudocriticality in antiferromagnetic spin chains
• Fermion Bag Approach for Hamiltonian Lattice Field Theories
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• Quantum Monte Carlo and Stabilizer States
• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• Deconfined criticality for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions
• Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions
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