Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1212.2944

Space group symmetries and low lying excitations of many-body systems at integer fillings

Rahul Roy

Published Dec 12, 2012• 11 citations
arXivHTMLPDF

Abstract

We show that many-body systems with conserved particle number which have the symmetries corresponding to a nonsymmorphic space group have low lying excitations for certain integer values of the particle number per unit cell. These results may be interpreted as a generalization of some band touching theorems to interacting systems.
DOI
10.48550/arxiv.1212.2944

Related papers

Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice

Masaki Oshikawa

In combination with Laughlin's treatment of the quantized Hall conductivity, the Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength, and particle statistics (Bose or Fermi), a finite excitation gap is possible only when the particle number per unit cell of the ground state is an integer.

arXiv:cond-mat/9911137•Physical Review Letters•Feb 14, 2000•411 citations

The origin of order in random matrices with symmetries

Calvin W. Johnson

From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with 'low' quantum numbers and symmetric, low-dimensional irreps, but there is no a priori reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J = 0 g.s. even for random two-body interactions.

arXiv:1206.5748•AIP conference proceedings•Jan 1, 2012•0 citations

Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems 1

Tohru Koma, Hal Tasaki

We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Néel order, and the Hubbard model with a (superconducting) off-diagonal long range order. In the corresponding finite system, the symmetry breaking is usually “obscured ” by “quantum fluctuation ” and one gets a symmetric ground state with a long range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of order N −1, where N denotes the number of the sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we prove bounds for their energy expectation values. The bounds establish that there exist ever increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant times N −1. A crucial feature of the particular low-lying

•Jan 1, 1997•51 citations

Parameter symmetries of quantum many-body systems

Pavel Cejnar, H. B. Geyer

We analyze the occurrence of dynamically equivalent Hamiltonians in the parameter space of general many-body interactions for quantum systems, particularly those that conserve the total number of particles. As an illustration of the general framework, the appearance of parameter symmetries in the interacting boson model 1 and their absence in the Ginocchio ${\mathrm{SO}}_{8}$ fermionic model are discussed.

arXiv:nucl-th/0110042•Physical Review C•Aug 14, 2001•4 citations

Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals

Dominic V. Else, Ryan Thorngren, T. Senthil

A system with charge conservation and lattice translation symmetry has a well-defined filling ν, which is a real number representing the average charge per unit cell.We show that if ν is fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems.The most powerful constraint comes about if ν is continuously tunable (i.e., the system is charge compressible), in which case, we show that the low-energy theory must have a very large emergent symmetry group-larger than any compact Lie group.An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved.We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics.We call a system with this property an ersatz Fermi liquid.We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger's theorem (which is thus extended to a large class of non-Fermi liquids) and periodic "quantum oscillations" in the response to an applied magnetic field.We also establish versions of Luttinger's theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators.Our work makes a connection between filling constraints and the theory of symmetry-protected topological phases, in particular through the concept of "'t Hooft anomalies."

arXiv:2007.07896•Physical Review X•Apr 6, 2021•90 citations

Universal Relation among the Many-Body Chern Number, Rotation Symmetry, and Filling

Akishi Matsugatani, Yuri Ishiguro, Ken Shiozaki +1 more

Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on the quantized Hall conductance of many-body systems with arbitrary interactions. Our results allow one to readily determine the many-body Chern number modulo a certain integer without performing any integrations, solely based on the rotation eigenvalues and the average particle density of the many-body ground state.

arXiv:1710.07012•Physical Review Letters•Feb 28, 2018•21 citations
From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with 'low' quantum numbers and symmetric, low-dimensional irreps, but there is no a priori reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J = 0 g.s. even for random two-body interactions.
We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Néel order, and the Hubbard model with a (superconducting) off-diagonal long range order. In the corresponding finite system, the symmetry breaking is usually “obscured ” by “quantum fluctuation ” and one gets a symmetric ground state with a long range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of order N −1, where N denotes the number of the sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we prove bounds for their energy expectation values. The bounds establish that there exist ever increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant times N −1. A crucial feature of the particular low-lying
We analyze the occurrence of dynamically equivalent Hamiltonians in the parameter space of general many-body interactions for quantum systems, particularly those that conserve the total number of particles. As an illustration of the general framework, the appearance of parameter symmetries in the interacting boson model 1 and their absence in the Ginocchio SO8{\mathrm{SO}}_{8}SO8​ fermionic model are discussed.
A system with charge conservation and lattice translation symmetry has a well-defined filling ν, which is a real number representing the average charge per unit cell.We show that if ν is fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems.The most powerful constraint comes about if ν is continuously tunable (i.e., the system is charge compressible), in which case, we show that the low-energy theory must have a very large emergent symmetry group-larger than any compact Lie group.An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved.We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics.We call a system with this property an ersatz Fermi liquid.We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger's theorem (which is thus extended to a large class of non-Fermi liquids) and periodic "quantum oscillations" in the response to an applied magnetic field.We also establish versions of Luttinger's theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators.Our work makes a connection between filling constraints and the theory of symmetry-protected topological phases, in particular through the concept of "'t Hooft anomalies."
Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on the quantized Hall conductance of many-body systems with arbitrary interactions. Our results allow one to readily determine the many-body Chern number modulo a certain integer without performing any integrations, solely based on the rotation eigenvalues and the average particle density of the many-body ground state.