Ground state projection of quantum spin systems in the valence bond basis

Abstract

A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations of the method to fermion systems are also discussed.

4+ pages, accepted for publication in Phys. Rev. Lett

References in corpus (2)

• "Deconfined" quantum critical points
• Deconfined quantum criticality and Neel order via dimer disorder

Cited by in corpus (87)

• The ALPS project release 1.3: open source software for strongly correlated systems
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Variational quantum Monte Carlo simulations with tensor-network states
• Entanglement entropy in quantum impurity systems and systems with boundaries
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Density matrix quantum Monte Carlo
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems
• The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
• Some formal results for the valence bond basis
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Valence Bond Entanglement Entropy
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Entanglement entropy from nonequilibrium work
• Entanglement scaling in two-dimensional gapless systems
• The plaquette phase of the square lattice quantum dimer model
• Engineering Surface Critical Behavior of (2+1)-Dimensional O(3) Quantum Critical Points
• Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
• Frustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
• Master equation approach to computing RVB bond amplitudes
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Method to characterize spinons as emergent elementary particles
• Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model
• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems
• Role of quantum fluctuations on spin liquids and ordered phases in the Heisenberg model on the honeycomb lattice
• Entanglement in gapless resonating valence bond states
• Velocity of excitations in ordered, disordered and critical antiferromagnets
• Nature of the low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets
• Stochastic series expansion simulation of the $t$-$V$ model
• Resonating valence bond physics is not always governed by the shortest tunneling loops
• Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid
• Off-Diagonal Expansion Quantum Monte Carlo
• Quantum dimer model for the spin-1/2 kagome Z2 spin liquid
• Quantum Monte Carlo studies of spinons in one-dimensional spin systems
• Exact Entanglement Studies of Strongly Correlated Systems: Role of Long-Range Interactions and Symmetries of the System
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Incremental SWAP Operator for Entanglement Entropy: Application for Exponential Observables in Quantum Monte Carlo Simulation
• Valence bond entanglement entropy of frustrated spin chains
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$
• Improved scaling of the entanglement entropy of quantum antiferromagnetic Heisenberg systems
• Neel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model
• Proximity effects in cold atom artificial graphene
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Valence bond solid phases in a cubic antiferromagnet
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin Liquids
• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Valence Bond Entanglement and Fluctuations in Random Singlet Phases
• Hardcore dimer aspects of the SU(2) Singlet wavefunction
• Correlated valence-bond states
• Emergent topological excitations in a two-dimensional quantum spin system
• Shared Information in Stationary States at Criticality
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• Definitions of entanglement entropy of spin systems in the valence-bond basis
• Monte Carlo Simulations of Interacting Anyon Chains
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• Antiferromagnetic order in systems with doublet $S_{\mathrm{tot}}=1/2$ ground states
• Neel and Valence Bond Crystal Order on a Distorted Kagome Lattice: Implications For Zn-Paratacamite
• Z4-U(1) crossover of the order parameter symmetry in a two-dimensional valence-bond-solid
• A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs
• Longitudinal Magnetization and specific heat of the anisotropic Heisenberg antiferromagnet on Honeycomb lattice
• Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Typicality at quantum-critical points
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Scaling of Entanglement Entropy in Point Contact Free Fermion Systems
• Comment on "Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets"
• Dynamical scaling behavior of the two-dimensional random singlet state in the random $Q$ model
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Entanglement of quantum spin systems: a valence-bond approach
• Scaling of Entanglement Entropy for the Heisenberg Model on Clusters Joined by Point Contacts
• Fibonacci sequence and its generalizations in doped quantum spin ladders
• Topological properties of a Valence-Bond-Solid
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
• Valence-Bond Quantum Monte Carlo Algorithms Defined on Trees