Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain

• URL: http://arxiv.org/abs/2205.04995v1
• Date: Tue, 10 May 2022 16:05:25 GMT
• Title: Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Authors: Julian Thoenniss and Alessio Lerose and Dmitry A. Abanin
• Abstract summary: We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF) We obtain explicit expressions of the wave function for a family of one-dimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. The approach can be applied to a number of experimental setups, including highly non-equilibrium transport via quantum dots and real-time formation of impurity-reservoir correlations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Describing a quantum impurity coupled to one or more non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. While historically the focus has been on the equilibrium properties of the impurity-reservoir system, recent experiments with mesoscopic and cold-atomic systems enabled studies of highly non-equilibrium impurity models, which require novel theoretical techniques. We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF). The efficiency of such a MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious "wave function" in the time domain. We obtain explicit expressions of this wave function for a family of one-dimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. While for initial states with short-range correlations we find temporal area-law scaling, Fermi-sea-type initial states yield logarithmic scaling with time, closely related to the real-space entanglement scaling in critical 1d systems. Furthermore, we describe an efficient algorithm for converting the explicit form of the reservoirs' IF to MPS form. Once the IF is encoded by a MPS, arbitrary temporal correlation functions of the interacting impurity can be efficiently computed, irrespective of its internal structure. The approach introduced here can be applied to a number of experimental setups, including highly non-equilibrium transport via quantum dots and real-time formation of impurity-reservoir correlations.

Related papers

• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Stochastic Schr\"odinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective [3.105656247358225]
  We develop a framework to simulate dynamics of Anderson-Holstein impurities coupled to a continuous fermionic bath. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and master equations.
  arXiv  Detail & Related papers  (2023-09-16T06:03:54Z)
• Neural-network quantum states for ultra-cold Fermi gases [49.725105678823915]
  This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture. We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions. Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases.
  arXiv  Detail & Related papers  (2023-05-15T17:46:09Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• An efficient method for quantum impurity problems out of equilibrium [0.0]
  We introduce an efficient method to simulate dynamics of an interacting quantum impurity coupled to non-interacting fermionic reservoirs. We apply our method to study quantum quenches and transport in an Anderson impurity model, including highly non-equilibrium setups. This approach will provide new insights into dynamical properties of mesoscopic devices and correlated materials.
  arXiv  Detail & Related papers  (2022-11-18T14:57:29Z)
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor [80.17270167652622]
  Quantum-body systems display rich phase structure in their low-temperature equilibrium states. We experimentally observe an eigenstate-ordered DTC on superconducting qubits. Results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.
  arXiv  Detail & Related papers  (2021-07-28T18:00:03Z)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• Scaling of temporal entanglement in proximity to integrability [0.0]
  We analytically compute the exact IM for a family of integrable Floquet models. We show that the IM exhibits area-law temporal entanglement scaling for all parameter values. Near criticality, a non-trivial scaling behavior of temporal entanglement is found.
  arXiv  Detail & Related papers  (2021-04-15T17:16:57Z)
• Influence functional of many-body systems: temporal entanglement and matrix-product state representation [0.0]
  Feynman-Vernon influence functional (IF) was originally introduced to describe the effect of a quantum environment on the dynamics of an open quantum system. We apply the IF approach to describe quantum many-body dynamics in isolated spin systems.
  arXiv  Detail & Related papers  (2021-03-25T10:41:15Z)
• Characterizing many-body localization via exact disorder-averaged quantum noise [0.0]
  Many-body localized (MBL) phases of disordered quantum many-particle systems have a number of unique properties. We characterize the quantum noise that a disordered spin system exerts on its parts via an influence matrix (IM) Viewed as a wavefunction in the space of trajectories of an individual spin, the IM exhibits slow scaling of temporal entanglement in the MBL phase.
  arXiv  Detail & Related papers  (2020-12-01T19:01:31Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.