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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• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• D-wave correlated Critical Bose Liquids in two dimensions
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• Finite Size Scaling of Mutual Information: A Scalable Simulation
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• Infinite-randomness quantum critical points induced by dissipation
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• Some formal results for the valence bond basis
• Theory of smeared quantum phase transitions
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• 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
• Ground States of the SU(N) Heisenberg Model
• Percolation quantum phase transitions in diluted magnets
• Spin Supersolid in Anisotropic Spin-One Heisenberg Chain
• Quantum phase transitions in bilayer SU(N) anti-ferromagnets
• Reading entanglement in terms of spin configurations in quantum magnets
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• Imaging bond order near non-magnetic impurities in square lattice antiferromagnets
• Impurity-induced frustration in correlated oxides
• Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
• Correlated valence-bond states
• Universal Scaling of the Neel Temperature of Near-Quantum-Critical Quasi-Two-Dimensional Heisenberg Antiferromagnets

Cited by in corpus (40)

• Provably efficient machine learning for quantum many-body problems
• Coherent and dissipative dynamics at quantum phase transitions
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• 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
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Spin nematic ground state of the triangular lattice S=1 biquadratic model
• 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
• Sign Problem in Quantum Monte Carlo Simulation
• 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
• 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
• Destroying a topological quantum bit by condensing Ising vortices
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
• 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
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Topological physics in quantum critical systems
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Metals get an awkward cousin
• Pseudocriticality in antiferromagnetic spin chains
• Geometric and computational aspects of chiral topological quantum matter
• 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
• Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions
• Roundtable: What can we learn about confinement and anomalous effects in QCD using analog systems?
• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d
• Deconfined criticality for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions
• Quantum Monte Carlo and Stabilizer States
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet