Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session Y20: Statistical Mechanics and Thermodynamics of Quantum Systems |
Hide Abstracts |
Sponsoring Units: DQI Chair: Takahiro Sagawa, University of Tokyo Room: LACC 308B |
Friday, March 9, 2018 11:15AM - 11:27AM |
Y20.00001: Saturation of entropy production in quantum many-body systems Kazuya Kaneko, Eiki Iyoda, Takahiro Sagawa Thermalization of isolated quantum systems has been of much interest in this decade. In this study, we investigate the second law of thermodynamics for isolated systems in the long time regime, where the initial state of a heat bath can be a pure state. First, we have rigorously proved that the entropy production, which is the sum of the change in the von Neumann entropy of a subsystem and the heat absorbed from a heat bath, saturates in the long-time regime for a broad class of initial states. Second, we have proved the non-negativity of the entropy production at saturation, by assuming the eigenstate thermalization hypothesis (ETH), which states that even a single energy eigenstate is thermal. We also numerically confirmed that the entropy production saturates at a non-negative value even when the initial state of a heat bath is a single energy eigenstate. Our results reveal fundamental properties of the entropy production in isolated quantum systems at late times. Reference: K. Kaneko, E. Iyoda, T. Sagawa, arXiv:1706.10112. |
Friday, March 9, 2018 11:27AM - 11:39AM |
Y20.00002: Atypicality of Most Few-Body Observables Ryusuke Hamazaki, Masahito Ueda The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a promising candidate to explain thermalization in isolated quantum systems. According to the typicality argument over the Haar measure, the maximum variations of such matrix elements should decrease exponentially with increasing the size of the system, which implies the ETH. We show, however, that the argument does not apply to most few-body observables for few-body Hamiltonians unless the width of the energy shell decreases exponentially with increasing the size of the system. |
Friday, March 9, 2018 11:39AM - 11:51AM |
Y20.00003: Large Deviation Analysis of Eigenstate Thermalization Hypothesis Toru Yoshizawa, Eiki Iyoda, Takahiro Sagawa A plausible mechanism of thermalization in isolated quantum systems is the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates have thermal properties. In the present work, we propose a new systematic numerical method to test the ETH by focusing on the large deviation property; By using exact numerical diagonalization, we directly calculate the ratio of athermal energy eigenstates in the energy shell. That ratio is exactly zero if the strong ETH is true, while a mathematical theory has only proved that the ratio is at most exponentially small in the system size. Our numerical results confirmed that the strong ETH indeed holds only for non-integrable systems, where we found that the finite-size scaling of the large deviation is double exponential. Furthermore, we numerically verified an expectation that the strong ETH is true for near-integrable systems, even with an infinitely small integrability-breaking term. |
Friday, March 9, 2018 11:51AM - 12:03PM |
Y20.00004: Scrambling of quantum information in quantum many-body systems Eiki Iyoda, Takahiro Sagawa Dynamics of quantum information in isolated systems is a topic of active researches, in terms of not only the foundation of statistical mechanics but also information paradox of black holes. Especially, it is significant to investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems, which can be quantified by the negativity of tripartite mutual information (TMI) or the decay rate of out-of-time-ordered correlator. |
Friday, March 9, 2018 12:03PM - 12:15PM |
Y20.00005: Writing the entanglement-geometry dictionary with quantum quenches and tensor networks Katharine Hyatt, James Garrison, Bela Bauer By examining tensor network representations of quantum states, it is possible to learn much about the entanglement structure of those states and about connections between various quantum and/or conformal field theories and relevant geometries. Building upon our previous work developing algorithms which generate tensor networks capturing important aspects of these dualities, we investigate other important aspects of the AdS/CFT correspondence. Performing global quenches on both pure and mixed states, we make contact with results for thermalization and the spread of entanglement in holographic systems. |
Friday, March 9, 2018 12:15PM - 12:27PM |
Y20.00006: Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos Xiao Chen, Andreas Ludwig We investigate the appearance of quantum chaos in a single many-body wave function by analyzing the statistical properties of the eigenvalues of its reduced density matrix ρA. We find that ρA is described by a so-called Wishart random matrix, which exhibits universal spectral correlations between eigenvalues. A simple and precise characterization of such correlations is a segment of linear growth at long times, recently called the ramp, of the spectral form factor. Numerical results for a generic non-integrable systems are found to exhibit an universal ramp identical to that appearing for a random pure state. In addition, we study the development of chaos in the wave function by letting an initial product state evolve under the unitary time evolution. We find that the ramp sets in as soon as the entanglement entropy begins to grow, and first develops at the top of the spectrum of ρA, subsequently spreads over the entire spectrum. Finally, we study a prethermalized regime described by a generalized Gibbs ensemble. We find that the prethermalized regime exhibits no chaos, as evidenced by the absence of a ramp , while the spectral correlations start to develop when the prethermalized regime finally relaxes at late times to the fully thermalized chaotic regime. |
Friday, March 9, 2018 12:27PM - 12:39PM |
Y20.00007: Interaction-induced transition in the quantum chaotic dynamics of a disordered metal Sergey Syzranov, Alexey Gorshkov, Victor Galitski We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups. |
Friday, March 9, 2018 12:39PM - 12:51PM |
Y20.00008: Is Temperature a Local Realistic Variable? Dervis Vural, Sushrut Ghonge Temperature is conventionally defined in terms of the number of "possible" microstates, given a set of macroscopic constraints such as total energy, volume and particle number. It is a remarkable achievement of statistical mechanics, that an information theoretical, combinatoric quantity can connect so well to physical observables, such as the hight of a mercury collumn, or the volume of a baloon. In this talk, we depart from this succesfull tradition. We start with the simple observation that if a large but finite system is split into two subsystems, their temperatures get entangled. As such, an operator description of temperature becomes necessary to avoid an EPR-type causality violation. In this new picture, temperature is subject to the constraints of quantum mechanics, where its measurement must necessarily accompany a wavefunction collapse into a "temperature eigenstate". Finally, we briefly discuss the experimental implications of this alternative, questionable view. |
Friday, March 9, 2018 12:51PM - 1:03PM |
Y20.00009: Thermal pure state path integral in isolated quantum system and emergent symmetry of thermodynamic entropy Shin-ichi Sasa, Sho Sugiura, Yuki Yokokura Thermodynamics and quantum mechanics are fundamental theories in physics. However, their relationship between their dynamics is not established yet; therefore we propose a theory connecting thermodynamical behavior to quantum mechanics. Our strategy is to construct a thermodynamical path integral. In thermodynamics, an equilibrium state of a system is represented by a point in the thermodynamic state space. In quantum mechanics, on the other hand, the time evolution of a system is described by the path integral. In this talk, we combine these two concepts for a thermally isolated quantum many-body system under a time-dependent external field. We formulate the unitary evolution of quantum states by an integral over paths in the thermodynamic state space. We call it thermal pure state path integral and find an emergent symmetry in it. In the thermal pure state path integral, we derive an effective action for trajectories in a thermodynamic state space, where entropy appears with its conjugate variable. In particular, for quasi-static operations, the symmetry for the uniform translation of the conjugate variable emerges; the thermodynamic entropy is characterized as a Noether invariant. It leads to entropy conservation. |
Friday, March 9, 2018 1:03PM - 1:15PM |
Y20.00010: Local temperature approximation of entanglement Hamiltonian Seyyed Mohammad Sadegh Vaezi, Zohar Nussinov, Abolhassan Vaezi The entanglement Hamiltoian, HE is related to the reduced density matrix associated with a sub-system A as: ρA = e-HE. An interesting question is (a) how local HE is, and (b) how is it related to the local Hamiltonian density of the system, 𝒽(x).It has been mathematically shown in the context of black-hole physics that for quantum systems with conformal symmetry, or those with Lorentz symmetry but at zero temperature, HE is local and can be written as HE = ∫x ∈ A (𝒽(x)/T(x)) dx, when entangling surfaces (boundaries between A and its complement) are flat. In this expression T(x) is a local temperature that diverges as 1/x near the entangling surfaces. This particular form of HE is known as the Rindler Hamiltonian. |
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