Abstract In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deformations, e.g., $T\overline{T}$ T T ¯ deformation, local bilinear operator deformation, and mass deformation. For $T\overline{T}$ T T ¯ deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian. As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature. Following the same perturbative strategy, we obtain the entanglement entropy of the free fermion vacuum state up to second-order by inserting a local bilinear operator deformation in a moving mirror setting. In the uniformly accelerated mirror, the first-order and second-order correction of entanglement entropy vanishes in the late time limit. For mass deformation, we derive the entanglement entropy up to first-order deformation and comment on the second-order correction.Abstract In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deformations, e.g., $$ T\overline{T} $$ T T ¯ deformation, local bilinear operator deformation, and mass deformation. For $$ T\overline{T} $$ T T ¯ deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian. As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature. Following the same perturbative strategy, we obtain the entanglement entropy of the free fermion vacuum state up to second-order by inserting a local bilinear operator deformation in a moving mirror setting. In the uniformly accelerated mirror, the first-order and second-order correction of entanglement entropy vanishes in the late time limit. For mass deformation, we derive the entanglement entropy up to first-order deformation and comment on the second-order correction.

arXiv:2207.06308Journal of High Energy PhysicsSep 30, 20229 citations

Calculation of Entanglement Entropy in Fermion Lattices

Michelle Storms, Rajiv R. P. Singh

Bulletin of the American Physical SocietyOct 4, 20130 citations

Entanglement in fermionic systems

Bei Zeng

Jan 1, 20120 citations

Link representation of the entanglement entropies for all bipartitions

Sudipto Singha Roy, Silvia N. Santalla, Germán Sierra +1 more

Abstract We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry associated with the entanglement structure of a quantum many-body state which may occasionally differ from the one suggested by the Hamiltonian of the system. Yet, the obtention of these entanglement links is a complex mathematical problem. In this work, we address this issue and propose several approximation techniques for matrix product states, free fermionic states, or in cases in which contiguous blocks are specially relevant. Along with this, we discuss the accuracy of the approximation for different types of states and partitions. Finally, we employ the link representation to discuss two different physical systems: the spin-1/2 long-range XXZ chain and the spin-1 bilinear biquadratic chain.Abstract We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry associated with the entanglement structure of a quantum many-body state which may occasionally differ from the one suggested by the Hamiltonian of the system. Yet, the obtention of these entanglement links is a complex mathematical problem. In this work, we address this issue and propose several approximation techniques for matrix product states, free fermionic states, or in cases in which contiguous blocks are specially relevant. Along with this, we discuss the accuracy of the approximation for different types of states and partitions. Finally, we employ the link representation to discuss two different physical systems: the spin-1/2 long-range XXZ chain and the spin-1 bilinear biquadratic chain.

arXiv:2103.08929Journal of Physics A Mathematical and TheoreticalJun 10, 202113 citations

How Dynamical Quantum Memories Forget

Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings

Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the ``mixed'' phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems — i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears — purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the ``mixed'' phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems — i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears — purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.

arXiv:2008.10611QuantumJan 17, 2021100 citations

Abstract In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deformations, e.g.,

T\overline{T}

T T ¯ deformation, local bilinear operator deformation, and mass deformation. For

T\overline{T}

T T ¯ deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian. As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature. Following the same perturbative strategy, we obtain the entanglement entropy of the free fermion vacuum state up to second-order by inserting a local bilinear operator deformation in a moving mirror setting. In the uniformly accelerated mirror, the first-order and second-order correction of entanglement entropy vanishes in the late time limit. For mass deformation, we derive the entanglement entropy up to first-order deformation and comment on the second-order correction.