Singular three-point density correlations in two-dimensional Fermi liquids

• URL: http://arxiv.org/abs/2602.16774v1
• Date: Wed, 18 Feb 2026 19:00:01 GMT
• Title: Singular three-point density correlations in two-dimensional Fermi liquids
• Authors: Pok Man Tam, Charles L. Kane,
• Abstract summary: We characterize a singularity in the equal-time three-point density correlations that is generic to two-dimensional interacting Fermi liquids.<n>For non-interacting Fermi gas, the coefficient of this singularity is given by the quantized Euler characteristic of the Fermi sea.<n>We show that this singularity persists in interacting Fermi liquids, and express the renormalization of the coefficient of Landau parameters.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We characterize a singularity in the equal-time three-point density correlations that is generic to two-dimensional interacting Fermi liquids. In momentum space where the three-point correlation is determined by two wavevectors $\mathbf{q}_1$ and $\mathbf{q}_2$, the singularity takes the form $|\mathbf{q}_1\times\mathbf{q}_2|$. We explain how this singularity is sharply defined in a long-wavelength collinear limit. For a non-interacting Fermi gas, the coefficient of this singularity is given by the quantized Euler characteristic of the Fermi sea, and it implies a long-range real space correlation favoring collinear configurations. We show that this singularity persists in interacting Fermi liquids, and express the renormalization of the coefficient of singularity in terms of Landau parameters, for both spinless and spinful Fermi liquids. Implications for quantum gas experiments are discussed.

Related papers

• Probing the Fermi Sea Topology in a Quantum Gas [0.0]
  Pauli's exclusion principle forces fermions to occupy distinct quantum states.<n>Recent theory predicts that for non-interacting fermions, the Euler characteristic of a $D$-dimensional Fermi sea is encoded in its $D$+1-point density correlations.
  arXiv  Detail & Related papers  (2025-11-28T17:01:50Z)
• A minimal tensor network beyond free fermions [39.847063110051245]
  This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems.<n>A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the partition sum of a classical statistical mechanics model to a Grassmann variable integral.<n>The resulting model is simple, featuring only two parameters: one governing spin-spin interaction and the other measuring the deviation from the free fermion limit.
  arXiv  Detail & Related papers  (2024-12-05T14:49:39Z)
• Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy [28.441455845282068]
  We demonstrate atom-resolved detection of itinerant bosonic $23$Na and fermionic $6$Li quantum gases.<n>In contrast to prior work on lattice-trapped gases, here we realize microscopy of quantum gases in the continuum.<n>Our technique opens the door to the atom-resolved study of strongly correlated quantum gases of bosons, fermions, and their mixtures.
  arXiv  Detail & Related papers  (2024-11-13T17:05:44Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Topological Density Correlations in a Fermi Gas [0.0]
  A Fermi gas of non-interacting electrons, or ultra-cold fermionic atoms, has a quantum ground state defined by a region of occupancy in momentum space known as the Fermi sea. The topology of a $D$ dimensional Fermi sea is physically encoded in the $D+1$ point equal time density correlation function. We make use of the topological $D+1$ point density correlation to reveal universal structures of the more general $M$ point density correlation functions in a $D$ dimensional Fermi gas.
  arXiv  Detail & Related papers  (2023-10-05T17:57:58Z)
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries [0.0]
  We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We show that such systems feature a non-trivial Hilbert space fragmentation for momenta incommensurate with the lattice. We conjecture that a Berezinskii-Kosterlitz-Thouless-type transition is driven by the unbinding of vortices along the temporal direction.
  arXiv  Detail & Related papers  (2023-07-17T18:14:54Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)
• Supersymmetry and multicriticality in a ladder of constrained fermions [0.0]
  Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration. In this paper we consider a superfrustrated model, which we deform from the supersymetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov class.
  arXiv  Detail & Related papers  (2021-05-10T13:46:56Z)
• Aspects of quantum information in finite density field theory [0.0]
  We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in $1+1$ space-time dimensions.
  arXiv  Detail & Related papers  (2020-11-02T19:00:26Z)
• Growth of mutual information in a quenched one-dimensional open quantum many body system [11.731315568079445]
  In a dissipative system, postquench information propagates solely through entangled pairs of quasiparticles having a finite lifetime. Remarkably, in spite of the finite lifetime of the quasiparticles, a finite steady-state value of the MI survives in times which is an artifact of nonvanishing two-point correlations.
  arXiv  Detail & Related papers  (2020-01-27T14:08:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.