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.

38 pages

References in corpus (7)

• 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
• What is an integrable quench?
• AdS/dCFT one-point functions of the SU(3) sector
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Integrable domain walls in ABJM theory
• Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory

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