Integrable Crosscap States: From Spin Chains to 1D Bose Gas

Abstract

The notion of a crosscap state, a special conformal boundary state first defined in 2d CFT, was recently generalized to 2d massive integrable quantum field theories and integrable spin chains. It has been shown that the crosscap states preserve integrability. In this work, we first generalize this notion to the Lieb-Liniger model, which is a prototype of integrable non-relativistic many-body systems. We then show that the defined crosscap state preserves integrability. We derive the exact overlap formula of the crosscap state and the on-shell Bethe states. As a byproduct, we prove the conjectured overlap formula for integrable spin chains rigorously by coordinate Bethe ansatz. It turns out that the overlap formula for both models take the same form as a ratio of Gaudin-like determinants with a trivial prefactor. Finally we study quench dynamics of the crosscap state, which turns out to be surprisingly simple. The stationary density distribution is simply a constant. We also derive the analytic formula for dynamical correlation functions in the Tonks-Girardeau limit.

arXiv comment38 pages

References in corpus (41)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Time evolution of local observables after quenching to an integrable model
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• The Quench Action
• What is an integrable quench?
• Analytic results for a quantum quench from free to hard-core one dimensional bosons
• One-point Functions in Defect CFT and Integrability
• One-point Functions in AdS/dCFT from Matrix Product States
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• AdS/dCFT one-point functions of the SU(3) sector
• A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
• 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model
• Expectation Values in the Lieb-Liniger Bose Gas
• Scalar one-point functions and matrix product states of AdS/dCFT
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit
• Overlaps of $q$-raised Néel states with XXZ Bethe states and their relation to the Lieb-Liniger Bose gas
• Overlaps between eigenstates of the XXZ spin-1/2 chain and a class of simple product states
• Overlaps of Partial Neel States and Bethe States
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Integrable Matrix Product States from boundary integrability
• Overlaps with arbitrary two-site states in the XXZ spin chain
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• Integrable domain walls in ABJM theory
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• Geometrizing non-relativistic bilinear deformations
• Crosscap States in Integrable Field Theories and Spin Chains
• On exact overlaps in integrable spin chains
• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory
• Irrelevant Deformations with Boundaries and Defects
• Exact Overlaps in the Lieb-Liniger Model from Coordinate Bethe Ansatz
• Integrable crosscaps in classical sigma models

Cited by in corpus (5)

• Extracting the Luttinger parameter from a single wave function
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Crosscap states and duality of Ising field theory in two dimensions
• Exact Quench Dynamics from Thermal Pure Quantum States