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arXiv:2407.10898

SVD Entanglement Entropy of Chiral Dirac Oscillators

Yuvraj Singh, Rabin Banerjee

Published Jul 15, 2024• 0 citations
arXivHTMLPDF

Abstract

We discuss the SVD entanglement entropy, which has recently come up as a successor to the pseudo entropy. This paper is a first of-its-kind application of SVD entanglement entropy to a system of chiral Dirac oscillators which prove to be a natural system to study the SVD formalism because the two chiral oscillator ground states can be taken as the pre-selected and post-selected states. We argue how this alternative for entanglement entropy is better and more intuitive than the von Neumann one to study quantum phase transition. It is shown that SVD entropy diverges at the critical point, matching von Neumann entropy in the left-handed regime but differing in the right-handed regime. We also provide as an illustrative example, a new generalized proof of the SVD entanglement entropy being log2 for a pair of Bell states that differ from each other by relative phases

DOI
10.48550/arxiv.2407.10898

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We discuss the SVD entanglement entropy, which has recently come up as a successor to the pseudo entropy. This paper is a first of-its-kind application of SVD entanglement entropy to a system of chiral Dirac oscillators which prove to be a natural system to study the SVD formalism because the two chiral oscillator ground states can be taken as the pre-selected and post-selected states. We argue how this alternative for entanglement entropy is better and more intuitive than the von Neumann one to study quantum phase transition. It is shown that SVD entropy diverges at the critical point, matching von Neumann entropy in the left-handed regime but differing in the right-handed regime. We also provide as an illustrative example, a new generalized proof of the SVD entanglement entropy being log2 for a pair of Bell states that differ from each other by relative phases
A bstract Pseudo-entropy and SVD entropy are generalizations of the entanglement entropy that involve post-selection. In this work we analyze their properties as measures on the spaces of quantum states and argue that their excess provides useful characterization of a difference between two (i.e. pre-selected and post-selected) states, which shares certain features and in certain cases can be identified as a metric. In particular, when applied to link complement states that are associated to topological links via Chern-Simons theory, these generalized entropies and their excess provide a novel quantification of a difference between corresponding links. We discuss the dependence of such entropy measures on the level of Chern-Simons theory and determine their asymptotic values for certain link states. We find that imaginary part of the pseudo-entropy is sensitive to, and can diagnose chirality of knots. We also consider properties of entropy measures for simpler quantum mechanical systems, such as generalized SU(2) and SU(1,1) coherent states, and tripartite GHZ and W states.
Abstract In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the Rényi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence.
The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of translational invariant lattice free fermion systems with two bands separated by a finite gap is investigated. We argue that, for one-dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band is equal to $\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}(\text{odd}\phantom{\rule{0.3em}{0ex}}\text{integer})$ and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than ln 2 (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two qubits. We also discuss how this lower bound is related to vanishing of the expectation value of a certain nonlocal operator which creates a kink in 1D systems.
A bstract Quantum informatic quantities such as entanglement entropy are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known entanglement entropy. It has many nice properties and is useful in the study of post-selection measurements. In this paper, one of our goals is to explore the properties of pseudo-entropy and study its effectiveness as a quantum chaos diagnostic, i.e., as a tool to distinguish between chaotic and integrable systems. Using various variants of the SYK model, we study the signal of quantum chaos captured in the pseudo-entropy and relate it to the spectral form factor (SFF) and local operator entanglement (LOE).
Entanglement entropy has proven to be a powerful probe of phenomena such as quantum chaos and phase transitions. Pseudo entropy is a recently proposed time-like generalization of an entanglement measure, motivated by de Sitter holography. In this work, we find that pseudo entropy can also serve as a novel probe for distinguishing topological phases of matter. For this, we consider the Su--Schrieffer--Heeger model as a representative example and investigate the averaged excess entropy ΔS12ΔS_{12}ΔS12​, defined as the difference between pseudo entropy and the average entanglement entropy, across the topological-to-trivial and trivial-to-topological phase transitions. When the two states are in the same phase, we find that $ ΔS_{12}$ is non-positive under periodic boundary conditions, while for open boundary conditions, it is non-positive only when the system is sufficiently large. Moreover, we analyze ground-state quench protocols for topology-crossing quenches and find that the imaginary pseudo entropy tracks the critical times predicted by the Fisher zeros.
We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition, which can be fully characterized. We obtain analytical expressions for the energy gap, order parameter, and canonical quantum fluctuations across the critical point. Moreover, we also discuss the effect of this phase transition on the statistics of the chiral bosonic ensemble, where its super- or sub-Poissonian nature can be controlled by means of external parameters. Finally, we study the entanglement properties between the degrees of freedom in the relativistic ground state, where an interesting transition between a biseparable and a genuinely tripartite entangled state occurs.