Spectrum-preserving deformations of integrable spin chains with open boundaries

Abstract

We discover a family of local deformations that leave part of the spectrum intact for strongly interacting and exactly solvable quantum many-body systems. Since the deformation preserves the Bethe Ansatz equations (BAE), it is dubbed the iso-BAE flow. Although all theories on the flow share the same BAE, the spectra are different. Part of the spectrum remains intact along the whole flow. Such states are protected by an emergent symmetry. The remaining parts of the spectrum change continuously along the flow and are doubly degenerate for even length spin chains. For odd length chains, the deformed spectrum also comprises doubly degenerate pairs apart from the sector with magnon number $(L+1)/2$, where $L$ is the length of the spin chain. We discuss the iso-BAE flow for the ${\mathrm{XXX}}_{1/2}$ model in detail and show that the iso-BAE flows exist for more general models including $q$-deformed XXZ as well as higher spin ${\mathrm{XXX}}_s$ spin chains.

7 pages, 2 figures (Supplemental Material 13 pages, 5 figures)

References in corpus (31)

• Time-dependence of correlation functions following a quantum quench
• Time evolution of local observables after quenching to an integrable model
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• The Quench Action
• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Integrable XYZ Spin Chain with Boundaries
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Correlation functions of the open XXZ chain I
• Correlation functions of the open XXZ chain II
• Boundary Critical Phenomena in the Three-State Potts Model
• Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions
• Fast analytic solver of rational Bethe equations
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
• Phases and dynamics of ultracold bosons in a tilted optical lattice
• On Generalized $Q$-systems
• On zero-remainder conditions in the Bethe ansatz
• Q-operators for the open Heisenberg spin chain
• Entanglement Hamiltonian of the 1+1-dimensional free, compactified boson conformal field theory
• Q-systems with boundary parameters
• Kondo effect in the isotropic Heisenberg spin chain
• On the reality of spectra of ${\mathbf{U}}_{\mathbf{q}}(\mathbf{s}{\mathbf{l}}_2)$-invariant XXZ Hamiltonians
• A Q-operator for open spin chains I: Baxter's TQ relation
• Spin-$s$ Rational $Q$-system
• Rational Q-systems at Root of Unity I. Closed Chains
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin

Cited by in corpus (1)

• Spin-$s$ $Q$-systems: Twist and Open Boundaries