Crosscap States in Integrable Field Theories and Spin Chains

Abstract

We study crosscap states in integrable field theories and spin chains in 1+1 dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the crosscap entropy, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov's staircase model to flows between D-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.

39 pages, 8 figures

References in corpus (11)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• What is an integrable quench?
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• The g-theorem and quantum information theory
• Poking Holes in AdS/CFT: Bulk Fields from Boundary States
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Universal entropy of conformal critical theories on a Klein bottle
• Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model
• Exact g-function flows from the staircase model
• On type 0 string theory in solvable RR backgrounds
• Boundary States and Anomalous Symmetries of Fermionic Minimal Models

Cited by in corpus (17)

• Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory
• Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• Holographic Dual of Crosscap Conformal Field Theory
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function
• Integrable Crosscap States: From Spin Chains to 1D Bose Gas
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Integrable crosscaps in classical sigma models
• 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
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Symmetric tensor scars with tunable entanglement from volume to area law
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• No boundary density matrix in elliptic de Sitter dS/${\mathbb{Z}}_2$
• Exact Quench Dynamics from Thermal Pure Quantum States