Massless Lifshitz Field Theory for Arbitrary
arXiv:2312.16284 · doi:10.1007/JHEP05(2024)284
Abstract
By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index . The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the -function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a -dependent radius scale for the Lifshitz background. This relation is consistent with the -dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.
arXiv comment28 pages, 6 figures, minor modifications and reference updated
References in corpus (51)
- A computable measure of entanglement
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Aspects of Holographic Entanglement Entropy
- Scaling of Entanglement close to a Quantum Phase Transitions
- The logarithmic negativity: A full entanglement monotone that is not convex
- Entanglement in a simple quantum phase transition
- Gravity Duals of Lifshitz-like Fixed Points
- Ghost Condensation and a Consistent Infrared Modification of Gravity
- Notes on Some Entanglement Properties of Quantum Field Theory
- Holographic Dual of BCFT
- A finite entanglement entropy and the c-theorem
- Aspects of AdS/BCFT
- Topological Order and Conformal Quantum Critical Points
- Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
- Ground state entanglement and geometric entropy in the Kitaev's model
- Lifshitz holography
- Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
- Shannon and entanglement entropies of one- and two-dimensional critical wave functions
- Comments on Holographic Entanglement Entropy and RG Flows
- Universal entanglement entropy in 2D conformal quantum critical points
- Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
- From classical to quantum dynamics at Rokhsar-Kivelson points
- Timelike entanglement entropy
- de Sitter space, extremal surfaces and "time-entanglement"
- Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
- Universal tripartite entanglement in one-dimensional many-body systems
- A New Proposal for Holographic BCFT
- On New Proposal for Holographic BCFT
- On the Null Energy Condition and Causality in Lifshitz Holography
- On holographic time-like entanglement entropy
- Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
- Holographic BCFT with Dirichlet Boundary Condition
- Entanglement Entropy in Lifshitz Theories
- -Theorem for Anisotropic RG Flows from Holographic Entanglement Entropy
- Time-like Entanglement Entropy in AdS/BCFT
- Constraints on RG Flows from Holographic Entanglement Entropy
- Correlation functions in theories with Lifshitz scaling
- Temporal Entanglement Entropy as a probe of Renormalization Group Flow
- Thermal Correlators in Holographic Models with Lifshitz scaling
- Conformal Boundary Condition and Massive Gravitons in AdS/BCFT
- Relating bulk to boundary entanglement
- Logarithmic Negativity in Quantum Lifshitz Theories
- Fix the dual geometries of deformed CFT and highly excited states of CFT
- Entanglement Entropy in Generalised Quantum Lifshitz Models
- Lifshitz entanglement entropy from holographic cMERA
- Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
- Entanglement and mutual information in two-dimensional nonrelativistic field theories
- Holographic two-point functions in a disorder system
- Finite-size versus finite-temperature effects in the critical long-range model