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DTSTART;TZID=Europe/Berlin:20230413T143000
DTEND;TZID=Europe/Berlin:20230413T143000
DTSTAMP:20260505T045351
CREATED:20250707T132030Z
LAST-MODIFIED:20250829T135526Z
UID:10000100-1681396200-1681396200@www.trr352.de
SUMMARY:A subpolynomial-time algorithm for the free energy of one-dimensional quantum systems in the thermodynamic limit
DESCRIPTION:We introduce a classical algorithm to approximate the free energy of local\, translation-invariant\, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e.\, the free energy at temperature T=0) for these systems is expected to be computationally hard even for quantum computers\, our algorithm runs for any fixed temperature T>0 in subpolynomial time\, i.e.\, in time O(1/E^c) for any constant c>0 where E is the additive approximation error. Previously\, the best known algorithm had a runtime that is polynomial in 1/E where the degree of the polynomial is exponential in the inverse temperature 1/T. Our algorithm is also particularly simple as it reduces to the computation of the spectral radius of a linear map. This linear map has an interpretation as a noncommutative transfer matrix and has been studied previously to prove results on the analyticity of the free energy and the decay of correlations. We also show that the corresponding eigenvector of this map gives an approximation of the marginal of the Gibbs state and thereby allows for the computation of various thermodynamic properties of the quantum system.
URL:https://www.trr352.de/event/a-subpolynomial-time-algorithm-for-the-free-energy-of-one-dimensional-quantum-systems-in-the-thermodynamic-limit/
LOCATION:Seminar room C4H33\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230427T160000
DTEND;TZID=Europe/Berlin:20230427T160000
DTSTAMP:20260505T045351
CREATED:20250707T131722Z
LAST-MODIFIED:20250829T135428Z
UID:10000098-1682611200-1682611200@www.trr352.de
SUMMARY:Magnetic properties of ground states in many-electron systems
DESCRIPTION:A mathematical understanding of the mechanism of metallic ferromagnetism still needs to be completed. In this talk\, the following three fundamental theorems on metallic ferromagnetism will be first outlined: the Marshall-Lieb-Mattis theorem\, the Lieb theorem\, and the stability theorem of Lieb ferrimagnetism. Next\, I will outline a mathematical framework within which these theorems can be unified. The theory is formulated using the standard forms of von Neumann algebras.
URL:https://www.trr352.de/event/magnetic-properties-of-ground-states-in-many-electron-systems/
LOCATION:Room C3N14\, Auf der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230427T160000
DTEND;TZID=Europe/Berlin:20230427T160000
DTSTAMP:20260505T045351
CREATED:20250707T131849Z
LAST-MODIFIED:20250829T135502Z
UID:10000099-1682611200-1682611200@www.trr352.de
SUMMARY:Classical simulation of short-time quantum dynamics
DESCRIPTION:Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo\, where the evolution is governed by a local Hamiltonian. For short times\, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables\, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting\, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular\, we establish a novel quantum speed limit\, a bound on dynamical phase transitions\, and a concentration bound for product states evolved for short times. Joint work with Dominik S. Wild (arXiv:2210.11490)
URL:https://www.trr352.de/event/classical-simulation-of-short-time-quantum-dynamics/
LOCATION:Seminar room C4H33\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
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