Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories

Abstract

We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find "chiralization", the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling ${\alpha }_c=2J/\pi$ with $J$ being the antiferromagnetic spin-exchange interaction. The central-charge $c=1$ conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition.

33 pages, 8 figures

References in corpus (33)

• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Composite fermion state of spin-orbit coupled bosons
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Excitonic topological order in imbalanced electron-hole bilayers
• Yang-Baxter and the Boost: splitting the difference
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• 2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity
• Lifshitz point at commensurate melting of 1D Rydberg atoms
• From entanglement generated dynamics to the gravitational anomaly and chiral central charge
• Multicriticality in Yang-Lee edge singularity
• Modular Commutators in Conformal Field Theory
• Fermionic propagators for 2D systems with singular interactions
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Theory of competing Chern-Simons orders and emergent phase transitions
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• From orbifolding conformal field theories to gauging topological phases
• Exact thermal properties of free-fermionic spin chains
• Chiral Anomaly in Euler Fluid and Beltrami Flow
• Chiral spin liquid state of strongly interacting bosons with a moat dispersion: a Monte Carlo simulation
• Emergence of Kac-Moody Symmetry in Critical Quantum Spin Chains
• Integrable Crosscap States: From Spin Chains to 1D Bose Gas
• Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• Mean-field theory for Heisenberg zigzag ladder: Ground state energy and spontaneous symmetry breaking
• Next-nearest-neighbor spin-spin and chiral-spin correlation functions in generalized XXX chain
• Can a spin chain relate combinatorics to number theory?
• Topological Quantum Computation on Supersymmetric Spin Chains

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• Topological physics in quantum critical systems
• Chiral vortex-line liquid of three-dimensional interacting Bose systems with moat dispersion
• Anomalous Dynamical Scaling at Topological Quantum Criticality