Intrinsic sign problem in fermionic and bosonic chiral topological matter
arXiv:2005.05566 · doi:10.1103/PhysRevResearch.2.043032
Abstract
The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. Here, we establish the existence of an intrinsic sign problem in a broad class of gapped, chiral, topological phases of matter. Within this class, we exclude the possibility of stoquastic Hamiltonians for bosons (or 'qudits'), and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The intrinsically sign-problematic class of phases we identify is defined in terms of topological invariants with clear observable signatures: the chiral central charge, and the topological spins of anyons. We obtain analogous results for phases that are spontaneously chiral, and present evidence for an extension of our results that applies to both chiral and non-chiral topological matter.
arXiv comment16 pages, 6 figures, 1 table (+ appendix: 8 pages, 2 figures). v2: updated Table I, additional minor changes
References in corpus (111)
- Topological insulators and superconductors
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Topological Field Theory of Time-Reversal Invariant Insulators
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Quantum Spin Liquids
- String-net condensation: A physical mechanism for topological phases
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Kitaev quantum spin liquid - concept and materialization
- The QCD thermal phase transition in the presence of a small chemical potential
- Applied Conformal Field Theory
- Fractional statistics in anyon collisions
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- Fermion Path Integrals And Topological Phases
- Observation of half-integer thermal Hall conductance
- A Constrained Path Monte Carlo Method for Fermion Ground States
- Machine learning quantum phases of matter beyond the fermion sign problem
- Fermionic Symmetry Protected Topological Phases and Cobordisms
- Quasi-particle Statistics and Braiding from Ground State Entanglement
- Quantized Thermal Transport in the Fractional Quantum Hall Effect
- Fractional topological insulators
- Quantum limit of heat flow across a single electronic channel
- Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
- A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
- Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
- Meron-Cluster Solution of Fermion Sign Problems
- Characterizing topological order by studying the ground states of an infinite cylinder
- Observed Quantization of Anyonic Heat Flow
- Synthetic Landau levels for photons
- Chiral d-wave superconductivity in doped graphene
- Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
- Fermionic SPT phases in higher dimensions and bosonization
- Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
- Quantum Monte Carlo study of the two-dimensional fermion Hubbard Model
- Numerical Study of Dense Adjoint Matter in Two Color QCD
- Thermal Transport in the Kitaev Model
- Gapped spin liquid with -topological order for kagome Heisenberg model
- Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
- Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
- Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
- A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
- Generalizations and limitations of string-net models
- Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
- Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
- Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
- Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
- Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
- Momentum polarization: an entanglement measure of topological spin and chiral central charge
- Projected entangled-pair states can describe chiral topological states
- Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
- Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
- Confinement transition of gauge theories coupled to massless fermions: emergent QCD and symmetry
- Monte Carlo Studies of Quantum Critical Metals
- Current Correlations from a Mesoscopic Anyon Collider
- Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
- Quantum critical behavior in three dimensional lattice Gross-Neveu models
- Easing the Monte Carlo sign problem
- Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the State
- Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
- A quantum Monte-Carlo method for fermions, free of discretization errors
- Boundary effective action for quantum Hall states
- Pairing in graphene: A quantum Monte Carlo study
- Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
- Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
- Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
- Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
- Geometric adiabatic transport in quantum Hall states
- On the Interpretation of Thermal Conductance of the nu=5/2 Edge
- Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
- Fractional Topological Insulators -- a Pedagogical Review
- A classification of 2D fermionic and bosonic topological orders
- On the Computational Complexity of Curing the Sign Problem
- Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
- Modular Matrices as Topological Order Parameter by Gauge Symmetry Preserved Tensor Renormalization Approach
- Fermion condensation and super pivotal categories
- Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
- Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
- Detecting two dimensional symmetry protected topological order in a ground state wave function
- Measuring Electromagnetic and Gravitational Responses of Photonic Landau Levels
- Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
- Guiding-center Hall viscosity and intrinsic dipole moment along edges of incompressible fractional quantum Hall fluids
- Symmetries and boundary theories for chiral Projected Entangled Pair States
- Comment on S. H. Simon, Interpretation of thermal conductance of the edge, arXiv:1801.09687
- Hall Viscosity of Hierarchical Quantum Hall States
- Universal Wave Function Overlap and Universal Topological Data from Generic Gapped Ground States
- How Quantum Are Non-Negative Wavefunctions?
- Protection of topological order by symmetry and many-body localization
- Probing topological superconductors with emergent gravity
- Sign problem in finite density lattice QCD
- Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
- Wavefunction positivization via automatic differentiation
- Monte Carlo Study of a U(1)xU(1) system with π-statistical Interaction
- Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions
- Intrinsic sign problems in topological quantum field theories
- Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG
- Boundary central charge from bulk odd viscosity - chiral superfluids
- Majorana Edge States for Z2 Topological Orders of the Wen-plaquette Model and the Toric-code Model
- Phases and phase transitions in a system with mutual statistics
- Hall Viscosity and Momentum Transport in Lattice and Continuum Models of the Integer Quantum Hall Effect in Strong Magnetic Fields
- Hall viscosity and conductivity of two-dimensional chiral superconductors
- Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
- Commuting-projector Hamiltonians for chiral topological phases built from parafermions
- Classical topological paramagnetism
- A search for correlation-induced adiabatic paths between distinct topological insulators
- A bosonic topological phase in a paired superfluid
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- Chiral central charge from a single bulk wave function
- Symmetry-protected sign problem and magic in quantum phases of matter
- Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
- Building models of topological quantum criticality from pivot Hamiltonians
- Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
- Fermion sign bounds theory in quantum Monte Carlo simulation
- Sign Problem in Quantum Monte Carlo Simulation
- Mitigating the fermion sign problem by automatic differentiation
- Robust Fermi liquid instabilities in sign problem-free models
- Defining a universal sign to strictly probe a phase transition
- Imaginary-time Mpemba effect in quantum many-body systems
- Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
- Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
- Geometric and computational aspects of chiral topological quantum matter
- Constraints from anti-unitary symmetries on phase diagrams of sign problem-free models
- Most two-dimensional bosonic topological orders forbid sign-problem-free quantum Monte Carlo: Nonpositive Gauss sum as an indicator
- Krylov complexity of many-body localization: Operator localization in Krylov basis
- Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
- Twisted quantum doubles are sign problem-free
- Complex path simulations of geometrically frustrated ladders