Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains

Abstract

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method.

4 pages, 3 figures

References in corpus (1)

• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

Cited by in corpus (83)

• Provably efficient machine learning for quantum many-body problems
• Entanglement entropy and the Berry phase in solid states
• Many-Body Order Parameters for Multipoles in Solids
• Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Inequivalent Berry phases for the bulk polarization
• Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains
• Phase diagram of the frustrated spin ladder
• Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
• Geometric phases induced in auxiliary qubits by many-body systems near its critical points
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Identification of topologically different valence bond states in spin ladders
• Scalar chiral ground states of spin ladders with four-spin exchanges
• Topological phase transition and ${\mathbb{Z}}_2$ index for $S=1$ quantum spin chains
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Geometric phases and criticality in spin systems
• On the dimerized phase in the cross-coupled antiferromagnetic spin ladder
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
• Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
• Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Classical many-particle systems with unique disordered ground states
• Anomalous magnetization of $S$=2 ferromagnetic-antiferromagnetic alternating chain with Ising anisotropy
• Path-integral Monte Carlo method for the local Z_2 Berry phase
• Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
• Bosonic integer quantum Hall effect as topological pumping
• Spin 3/2 dimer model
• Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction
• Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study
• Geometric Phase and Quantum Phase Transition : Two-Band Model
• Entanglement properties of the Haldane phases: A finite system-size approach
• Twisted Order Parameter applied to Dimerized Ladders
• Low-energy properties of two-leg spin-1 antiferromagnetic ladders with commensurate external fields and their extensions
• Polarization amplitude near quantum critical points
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Automorphic equivalence preserves the split property
• Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
• Rigorous Index Theory for One-Dimensional Interacting Topological Insulators
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Plateau transitions of spin pump and bulk-edge correspondence
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Fractionally quantized Berry phases of magnetization plateaux in spin-$1/2$ Heisenberg multimer chains
• Translation constraints on quantum phases with twisted boundary conditions
• Extraction of topological information in Tomonaga-Luttinger liquids
• Many-body multipole index and bulk-boundary correspondence
• Ground-State Phase Diagram of the Bond-Alternating $S=2$ Quantum Spin Chain with the $XXZ$ and On-Site Anisotropies -- Symmetry Protected Topological Phase versus Trivial Phase
• Gappability Index for Quantum Many-Body Systems
• Fractional corner magnetization of collinear antiferromagnets
• Electronic polarization in non-Bloch band theory
• Spin-1 chain with spin-1/2 excitations in the bulk
• Quantum phase transitions of spin chiral nanotubes
• Observation of average topological phase in disordered Rydberg atom array
• Randomness-driven quantum phase transition in bond-alternating Haldane chain
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder
• Dynamical structure factors of S=1 bond-alternating Heisenberg chains
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
• Critical spin-$\frac{1}{2}$ tetramer compound CuInVO${}_5$: Exploring the vicinity of two multimerized singlet states
• Topological Phases in Half-Integer Higher Spin $J_1$-$J_2$ Heisenberg Chains
• Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• Correlated Zak insulator in organic antiferromagnets
• The geometric phase and the dynamics of quantum phase transition induced by a linear quench
• The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped
• A little bit of self-correction
• Quantum Computing with sine-Gordon Qubits
• Ground state of antiferromagnetic Heisenberg two-leg ladder in terms of the valence-bond solid picture
• Promising regimes for the observation of topological degeneracy in spin chains
• Identification of gapless phases by a twisting operator
• On the ground-state properties of antiferromagnetic half-integer spin chains with long-range interactions
• Localization detection based on quantum dynamics
• Gapless points of dimerized quantum spin chains: analytical and numerical studies
• Diagnosing energy gap in quantum spin liquids via polarization amplitude
• Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities
• Geometric Effects on Tunneling in Driven Quantum Systems
• Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension
• Observation of Localization Using a Noisy Quantum Computer
• On effects of regular S=1 dilution of S=1/2 antiferromagnetic Heisenberg chains by a quantum Monte Carlo simulation
• The Lattice $\beta$-function of Quantum Spin Chains
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems