Quantum entanglement, lacking any classical counterpart, provides a fundamental new route to characterize the quantum nature of many-body states. In this work, we discuss an implementation of a new path integral method [Phys. Rev. Res. 2, 033505 (2020)] for fermions to compute entanglement for extended subsystems in the Hubbard model within dynamical mean-field theory (DMFT) in one and two dimensions. The new path integral formulation measures entanglement by applying a ``kick'' to the underlying interacting fermions. We show that the R\'enyi entanglement entropy can be extracted efficiently within the DMFT framework by integrating over the strength of the kick term. Using this method, we compute the second R\'enyi entropy as a function of subsystem size for metallic and Mott insulating phases of the Hubbard model. We explore the thermal entropy to entanglement crossover in the subsystem R\'enyi entropy in the correlated metallic phase. We show that the subsystem-size scaling of the second R\'enyi entropy is well described by the crossover formula which interpolates between the volume-law thermal R\'enyi entropy and the universal boundary-law R\'enyi entanglement entropy with logarithmic violation, as predicted by conformal field theory. We also study the mutual information across the Mott metal-insulator transition.
The Sachdev-Ye-Kitaev (SYK) model is a quantum-mechanical model of fermions interacting with
q-body random couplings. For
q=2, it describes free particles and is nonchaotic in the many-body sense, while for
q>2 it is strongly interacting and exhibits many-body chaos. In this work we study the entanglement entropy (EE) of the
SYKq models for a bipartition of
N real or complex fermions into subsystems containing
2m real/
m complex fermions and $N\ensuremath{-}2m$/$N\ensuremath{-}m$ fermions in the remainder. For the free model
SYK2, we obtain an analytic expression for the EE, derived from the $\ensuremath{\beta}$-Jacobi random matrix ensemble. Furthermore, we use the replica trick and path-integral formalism to show that the EE is maximal when one subsystem is small, i.e., $m\ensuremath{\ll}N$, for arbitrary
q. We also demonstrate that the EE for the SYK4 model is noticeably smaller than the Page value when the two subsystems are comparable in size, i.e.,
m/N is
O(1). Finally, we explore the EE for a model with both SYK2 and SYK4 interactions and find a crossover from SYK2 (low-temperature) to SYK4 (high-temperature) behavior as we vary energy.
The subsystem-size dependence of ground-state entanglement entropy and its crossover to thermal entropy as a function of temperature are well understood for one-dimensional (1D) gapless systems described by conformal field theory (CFT), and for free fermions with a Fermi surface in any dimension. However, little is known about the entanglement entropy for gapless fermionic systems without quasi-particles, such as a strange metal. Here we study the entanglement entropy of fermions in a solvable large-
N 1D lattice model akin to the Yukawa-Sachdev-Ye-Kitaev (Yukawa SYK) model. In this model, two Fermi points are coupled to scalar bosons via spatially random Yukawa interactions, providing a solvable model of a strange metal when the bosons become critical at a quantum critical point. We exactly compute the second Rényi entropy of fermions in a spatial subregion in this model. Our results unravel crucial role of intra-subregion entanglement between fermionic and bosonic degrees of freedom along with the inter-subregion entanglement in understanding the ground states of such strongly coupled fermion-boson systems. We show that the crossover from thermal entropy to entanglement entropy, is captured by a single scaling ansatz, that collapses the second Rényi entropy of fermions for different subregion sizes and temperatures into a single universal curve. We further show that the universal scaling curve for the critical strange metal is well described by the standard CFT formula, albeit with an effective central charge substantially larger than the non-interacting value.
Abstract Sachdev-Ye-Kitaev (SYK) is a concrete solvable model with non-Fermi liquid behavior and maximal chaos. In this work, we study the entanglement Rényi entropy for the subsystems of the SYK model in the Kourkoulou-Maldacena states. We use the path-integral approach and take the saddle point approximation in the large-N limit. We find a first-order transition exist when tuning the subsystem size for the q = 4 case, while it is absent for the q = 2 case. We further study the entanglement dynamics for such states under the real-time evolution for noninteracting, weakly interacting and strongly interacting SYK(-like) models.
The Sachdev-Ye-Kitaev model is an N N -modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large- N N limit. The results are consistent with exact diagonalization and can be well approximated by thermal entropy with an effective temperature when subsystem size M\leq N/2 M ≤ N / 2 . We also consider generalizations of the SYK model with quadratic random hopping term or U(1) U ( 1 ) charge conservation.
We formulate a new ``Wigner characteristics''-based method to calculate entanglement entropies of subsystems of Fermions using Keldysh field theory. This bypasses the requirements of working with complicated manifolds for calculating R\'enyi entropies for many-body systems. We provide an exact analytic formula for R\'enyi and von Neumann entanglement entropies of noninteracting open quantum systems, which are initialized in arbitrary Fock states. We use this formalism to look at entanglement entropies of momentum Fock states of one-dimensional Fermions. We show that the entanglement entropy of a Fock state can scale either logarithmically or linearly with subsystem size, depending on whether the number of discontinuities in the momentum distribution is smaller or larger than the subsystem size. We also use this formalism to describe entanglement dynamics of an open quantum system starting with a single domain wall at the center of the system. Using entanglement entropy and mutual information, we understand the dynamics in terms of coherent motion of the domain wall wavefronts, creation and annihilation of domain walls, and incoherent exchange of particles with the bath.