ProjectFinite-Size Criteria for Spectral Gaps in Quantum Lattice Systems

Basic data

Title:
Finite-Size Criteria for Spectral Gaps in Quantum Lattice Systems
Duration:
01/01/2023 to 31/12/2026
Abstract / short description:
A central question in the study of quantum lattice systems is whether the Hamiltonian operator exhibits a spectral gap above the ground state sector in the thermodynamic limit. Existence of a spectral gap is at the heart of the classification of quantum phases and it has far-reaching consequences for the low-energy physics of the system, specifically for the ground state correlation properties. Many open problems in mathematical physics concern the existence of a spectral gap for the Hamiltonian operator, but the mathematical techniques for rigorously deriving spectral gaps are limited. This research proposal focuses on the approach of deriving spectral gaps via finite-size criteria. Finite-size criteria allow to rigorously conclude the existence of a spectral gap at arbitrary system size from a single finite-size calculation. They have recently emerged as an effective tool for deriving spectral gaps in higher-dimensional frustration-free quantum spin systems. This proposal is guided by two related questions: (a) What is the wider scope of finite-size criteria? Here we explore long-range spin systems and bosonic lattice gases, for example. (b) In which concrete models can we verify finite-size criteria? Here we consider Motzkin Hamiltonians and certain families of random Hamiltonians, for example.
Keywords:
quantum spin systems
spectral gaps
quantum lattice systems
quantum many-body models
finite-size criteria

Involved staff

Managers

Department of Mathematics
Faculty of Science
SFB-TR 352 - Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
Collaborative research centers and transregios

Other staff

Department of Mathematics
Faculty of Science

Local organizational units

Department of Mathematics
Faculty of Science
University of Tübingen

Funders

Bonn, Nordrhein-Westfalen, Germany
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