We explore the dynamics of the entanglement entropy near equilibrium in highly entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.We explore the dynamics of the entanglement entropy near equilibrium in highly entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.

arXiv:1501.01315Physical Review EJun 19, 201548 citations

Entanglement Hamiltonians for quantum spin chains

Ronny Thomale, Stephan Rachel, Daniel P. Arovas +1 more

Bulletin of the American Physical SocietyMar 24, 20110 citations

Entanglement in Spin Chains

K. Sengupta

arXiv:2109.02657Quantum science and technologyJan 1, 202232 citations

Dominant superconducting correlations in a Luttinger liquid induced by spin fluctuations

Niels Henrik Aase, Asle Sudbø

We study spin-fluctuation mediated divergent superconducting fluctuations in a Luttinger liquid proximity-coupled to a spin chain. Our study provides insight into how spin fluctuations can induce superconductivity in a strongly correlated non-Fermi liquid with repulsive electronic interactions only. The electrons in the system are governed by the Extended Hubbard Hamiltonian and are coupled to a chain of localized spins modeled by the spin- $\frac{1}{2}\phantom{\rule{4pt}{0ex}}XX$ Hamiltonian. Using a multichannel Luttinger liquid approach, we determine the phase diagram of the metal chain. We find that spin-polarized triplet superconducting correlations persist for repulsive electronic interactions for sufficiently large interchain couplings.We study spin-fluctuation mediated divergent superconducting fluctuations in a Luttinger liquid proximity-coupled to a spin chain. Our study provides insight into how spin fluctuations can induce superconductivity in a strongly correlated non-Fermi liquid with repulsive electronic interactions only. The electrons in the system are governed by the Extended Hubbard Hamiltonian and are coupled to a chain of localized spins modeled by the spin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}XX$ Hamiltonian. Using a multichannel Luttinger liquid approach, we determine the phase diagram of the metal chain. We find that spin-polarized triplet superconducting correlations persist for repulsive electronic interactions for sufficiently large interchain couplings.

arXiv:2210.09098Physical review. B./Physical review. BDec 8, 20220 citations

Entanglement spectrum in Spin Chains

Ronny Thomale, Daniel P. Arovas, Bogdan Andrei Bernevig

Bulletin of the American Physical SocietyMar 16, 20101 citation

Identifying a correlated spin fluctuation in an entangled spin chain subject to a quantum phase transition

Kaoru Shimizu, 康弘都倉

This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix \ensuremath{\rho} of the spin pair from the ground state |\ensuremath{\Psi}⟩ of a spin chain, and then identify the quantum correlation part ${\ensuremath{\rho}}_{q}$ embedded in \ensuremath{\rho}. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ${\ensuremath{\rho}}_{q}$ as $W|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}|$ with the weight $W$ $\ensuremath{\le}1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix \ensuremath{\rho} of the spin pair from the ground state |\ensuremath{\Psi}⟩ of a spin chain, and then identify the quantum correlation part ${\ensuremath{\rho}}_{q}$ embedded in \ensuremath{\rho}. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ${\ensuremath{\rho}}_{q}$ as $W|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}|$ with the weight $W$ $\ensuremath{\le}1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.

Physical Review EDec 28, 20150 citations

\frac{1}{2}\phantom{\rule{4pt}{0ex}}XX

Hamiltonian. Using a multichannel Luttinger liquid approach, we determine the phase diagram of the metal chain. We find that spin-polarized triplet superconducting correlations persist for repulsive electronic interactions for sufficiently large interchain couplings.

W

$\ensuremath{\le}1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.