Nonequilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for nonequilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multipoint correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large- $N$ Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and nonlocal Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large- $N$ results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the noninteracting ${\mathrm{SYK}}_{2}$ model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting ${\mathrm{SYK}}_{q\ensuremath{\ge}4}$ model thermalizes slower than the noninteracting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the nonlocal and/or multipoint quantum correlations that relax as the system thermalizes.Nonequilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for nonequilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multipoint correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large-$N$ Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and nonlocal Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large-$N$ results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the noninteracting ${\mathrm{SYK}}_{2}$ model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting ${\mathrm{SYK}}_{q\ensuremath{\ge}4}$ model thermalizes slower than the noninteracting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the nonlocal and/or multipoint quantum correlations that relax as the system thermalizes.

arXiv:2504.13258Physical review. B./Physical review. BOct 16, 20252 citations

Exactly solvable model of fermions with disorder

Alexei M. Tsvelik

Nonperturbative results are obtained for multipoint correlation functions of the model of (2+1)-dimensional relativistic fermions in a random non-Abelian gauge potential. At zero frequencies the model is a critical theory with power law behavior of correlation functions. The average distance between the energy levels scales as ${\mathit{L}}^{\mathrm{\ensuremath{-}}2+1/\mathit{N}2}$, where L is the system's size and N is the number of components of the fermionic field. We calculate the diffusion propagator and show that the dc conductivity for this model is finite.Nonperturbative results are obtained for multipoint correlation functions of the model of (2+1)-dimensional relativistic fermions in a random non-Abelian gauge potential. At zero frequencies the model is a critical theory with power law behavior of correlation functions. The average distance between the energy levels scales as ${\mathit{L}}^{\mathrm{\ensuremath{-}}2+1/\mathit{N}2}$, where L is the system's size and N is the number of components of the fermionic field. We calculate the diffusion propagator and show that the dc conductivity for this model is finite.

arXiv:cond-mat/9409039Physical review. B, Condensed matterApr 15, 199523 citations

Multi-particle entanglement

Dirk Bouwmeester, Jian-Wei Pan, Matthew Daniell +2 more

Springer eBooksJun 1, 20012 citations

Entanglement contour in the disordered electronic systems

Niaz Ali Khan, Munsif Jan, Gao Xianlong

Physica E Low-dimensional Systems and NanostructuresSep 30, 20225 citations

General bounds for sender-receiver capacities in multipoint quantum communications

Riccardo Laurenza, Stefano Pirandola

We investigate the maximum rates for transmitting quantum information, distilling entanglement, and distributing secret keys between a sender and a receiver in a multipoint communication scenario, with the assistance of unlimited two-way classical communication involving all parties. First we consider the case where a sender communicates with an arbitrary number of receivers, a so-called quantum broadcast channel. Here we also provide a simple analysis in the bosonic setting where we consider quantum broadcasting through a sequence of beamsplitters. Then, we consider the opposite case where an arbitrary number of senders communicate with a single receiver, a so-called quantum multiple-access channel. Finally, we study the general case of all-in-all quantum communication where an arbitrary number of senders communicate with an arbitrary number of receivers. Since our bounds are formulated for quantum systems of arbitrary dimension, they can be applied to many different physical scenarios involving multipoint quantum communication.We investigate the maximum rates for transmitting quantum information, distilling entanglement, and distributing secret keys between a sender and a receiver in a multipoint communication scenario, with the assistance of unlimited two-way classical communication involving all parties. First we consider the case where a sender communicates with an arbitrary number of receivers, a so-called quantum broadcast channel. Here we also provide a simple analysis in the bosonic setting where we consider quantum broadcasting through a sequence of beamsplitters. Then, we consider the opposite case where an arbitrary number of senders communicate with a single receiver, a so-called quantum multiple-access channel. Finally, we study the general case of all-in-all quantum communication where an arbitrary number of senders communicate with an arbitrary number of receivers. Since our bounds are formulated for quantum systems of arbitrary dimension, they can be applied to many different physical scenarios involving multipoint quantum communication.

arXiv:1603.07262Physical Review ASep 12, 201791 citations

N

Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and nonlocal Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large-

N

results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the noninteracting

{\mathrm{SYK}}_{2}

model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting ${\mathrm{SYK}}_{q\ensuremath{\ge}4}$ model thermalizes slower than the noninteracting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the nonlocal and/or multipoint quantum correlations that relax as the system thermalizes.