About

Bruno Nachtergaele's general research area is Mathematical Physics, with a focus on a variety of problems in equilibrium and non-equilibrium statistical mechanics. His current research interests include the study of ground states and dynamics of quantum spin systems, the stability and low-lying excitations of quantum interfaces, hydrodynamic limits of quantum many-body systems, and the properties of the dynamics of quantum lattice systems. His work finds applications in Condensed Matter Physics, Nanotechnology, Quantum Information Theory, and Quantum Computation.

Research topics

• Mathematics
• Statistical physics
• Physics
• Theoretical physics
• Quantum mechanics

Selected publications

• Recursive spectral relations and the charge vs neutral gap in fractional quantum Hall systems

  Journal of Mathematical Physics · 2026-01-01

  article

  We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions.

  PublisherDOI

• Mathematical Results in Quantum Mechanics

  Advanced series in mathematical physics · 2025-09-15

  book
  PublisherDOI

• Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems

  ArXiv.org · 2025-07-24

  preprintOpen access

  We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions.

  PublisherOA PDFDOI

• Special issue honouring Mary Beth Ruskai

  Letters in Mathematical Physics · 2025-01-04

  articleOpen access
  PublisherOA PDFDOI

• The charge gap is greater than the neutral gap in fractional quantum Hall systems

  arXiv (Cornell University) · 2024-10-15

  preprintOpen access

  Past studies of fractional quantum Hall systems have found that the charge gap dominates the neutral gap for all relevant parameter choices. We report a wide-ranging proof that this domination is in fact a universal property of any Hamiltonian that satisfies a few simple structural properties: translation-invariance, charge conservation, dipole conservation, and a fractionally filled ground state. The result applies to both fermions and bosons. Our main tool is a new mathematical scheme, the gap comparison method, which provides a sequence of inequalities that relate the spectral gaps in successive particle number sectors. Our finding sheds new light on dipole conservation's profound effects on many-body physics.

  PublisherOA PDFDOI

• Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

  Letters in Mathematical Physics · 2024-02-03 · 13 citations

  articleOpen access1st authorCorresponding

  Abstract We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain this result, we extend the Bravyi–Hastings–Michalakis strategy so it can be applied to perturbations of the GNS Hamiltonian of the infinite-system ground state.

  PublisherOA PDFDOI

• Preface — Special Issue on Mathematical Results in Quantum Mechanics (QMath15)

  Reviews in Mathematical Physics · 2024-09-12

  review
  PublisherDOI

• Dynamical abelian anyons with bound states and scattering states

  arXiv (Cornell University) · 2023-03-13

  preprintOpen access

  We introduce a family of quantum spin Hamiltonians on $\mathbb{Z}^2$ that can be regarded as perturbations of Kitaev's abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the sector with one electric charge and one magnetic flux and show that the spectrum in this sector consists of both bound states and scattering states of abelian anyons. Concretely, we have defined a family of lattice models in which abelian anyons arise naturally as finite-size quasi-particles with non-trivial dynamics that consist of a charge-flux pair. In particular, the anyons exhibit a non-trivial holonomy with a quantized phase, consistent with the gauge and duality symmetries of the Hamiltonian.

  PublisherOA PDFDOI

• Remembrances of Derek William Robinson, June 25, 1935–August 31, 2021

  Notices of the American Mathematical Society · 2023-08-10

  articleOpen access
  PublisherDOI

• Dynamical Abelian anyons with bound states and scattering states

  Journal of Mathematical Physics · 2023-07-01 · 3 citations

  article

  We introduce a family of quantum spin Hamiltonians on Z2 that can be regarded as perturbations of Kitaev’s Abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the sector with one electric charge and one magnetic flux and show that the spectrum in this sector consists of both bound states and scattering states of Abelian anyons. Concretely, we have defined a family of lattice models in which Abelian anyons arise naturally as finite-size quasi-particles with non-trivial dynamics that consist of a charge-flux pair. In particular, the anyons exhibit a non-trivial holonomy with a quantized phase, consistent with the gauge and duality symmetries of the Hamiltonian.

  PublisherDOI

Recent grants

• Dynamics, Ground States, and Elementary Excitations of Quantum Many-Body Systems

  NSF · $375k · 2015–2019

• Dynamics and Ground States in Quantum Statistical Mechanics

  NSF · $365k · 2010–2014

• Equilibrium and Non-Equilibrium Quantum Statistical Mechanics

  NSF · $207k · 2003–2007

• Quasi-Locality Properties of Quantum Many-Body Dynamics and Applications

  NSF · $368k · 2018–2022

• Equilibrium and Non-Equilibrium Statistical Mechanics

  NSF · $142k · 2006–2009

Frequent coauthors

• Robert Sims

  33 shared

• M. Fannes

  KU Leuven

  18 shared

• Shannon Starr

  13 shared

• Amanda Young

  University of Illinois Urbana-Champaign

  12 shared

• Tohru Koma

  10 shared

• Reinhard F. Werner

  10 shared

• Tom Michoel

  University of Bergen

  9 shared

• Valentin A. Zagrebnov

  8 shared