Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
arXiv:2205.11123 · doi:10.1088/1367-2630/acd8e8
Abstract
An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) in spatial dimensions shows a violation of the area-law in real-space entanglement entropy of a subsystem (of length ), , widely believed to be a hallmark signature of the ground state of a gapless quantum critical system of interacting fermions. In this work, we apply a renormalisation group approach to a prototype of the FL in momentum (or, )-space, unveiling thereby the RG relevant quantum fluctuations (due to forward and tangential scattering) from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of the area-law in gapless electronic liquids for a subsystem defined within a -space window (of size ) proximate to the Fermi surface, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to the gapped quantum liquids emergent from the destabilisation of the Fermi surface by quantum fluctuations arising from backscattering processes. Indeed, we find that the -space entanglement signatures of gapped quantum liquids appear to be governed by the nature of the Fermi surface (e.g., nested or not) from which they emerge, as well as the nature of their parent gapless metallic liquid (e.g., FL, MFL etc.). This is confirmed by our finding an enhanced entanglement entropy for the nodal MFL present at the quantum critical point recently discovered in the 2D Hubbard model at optimal hole-doping. Our work thus paves the way for an entanglement based classification of quantum liquids emergent from the criticality of interacting fermionic matter.
arXiv comment9 pages, 6 figures, 77 References in main manuscript. Supplementary Materials also included
References in corpus (88)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Entanglement Entropy and Quantum Field Theory
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Aspects of Holographic Entanglement Entropy
- Scaling of Entanglement close to a Quantum Phase Transitions
- String-net condensation: A physical mechanism for topological phases
- Entanglement in a simple quantum phase transition
- Renormalization Group Approach to Interacting Fermions
- Quantum entanglement in condensed matter systems
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Violation of the entropic area law for Fermions
- Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
- Quantum Noise as an Entanglement Meter
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Bipartite Fluctuations as a Probe of Many-Body Entanglement
- Entanglement entropy: holography and renormalization group
- Entanglement Entropy and the Fermi Surface
- Entanglement scaling in critical two-dimensional fermionic and bosonic systems
- Momentum-space entanglement and renormalization in quantum field theory
- The entanglement entropy of one-dimensional gases
- Entanglement entropy of excited states
- General Relation between Entanglement and Fluctuations in One Dimension
- Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
- Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
- Quantum Disentangled Liquids
- Universality in the full counting statistics of trapped fermions
- Exact relations between particle fluctuations and entanglement in Fermi gases
- Exact holographic mapping and emergent space-time geometry
- Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
- Detecting Quantum Critical Points using Bipartite Fluctuations
- Entanglement Entropy of Scattering Particles
- Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
- Universal crossovers between entanglement entropy and thermal entropy
- Towards measuring Entanglement Entropies in Many Body Systems
- Algebraic construction of current operators in integrable spin chains
- Entanglement entropies in free fermion gases for arbitrary dimension
- Quantum Impurity Entanglement
- Quantum noise and entanglement generated by a local quantum quench
- Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
- Entanglement scaling in two-dimensional gapless systems
- From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
- Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
- Coarse Grained Quantum Dynamics
- A note on the Full Counting Statistics of paired fermions
- Entanglement and particle correlations of Fermi gases in harmonic traps
- A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy
- Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
- Renyi entropy, mutual information, and fluctuation properties of Fermi liquids
- Conformal Field Theory on the Fermi Surface
- Topological interpretation of Luttinger theorem
- Exact holographic mapping in free fermion systems
- Holographic interpretations of the renormalization group
- Fluctuations and Entanglement spectrum in quantum Hall states
- Entanglement structure of the Hubbard model in momentum space
- Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics
- Entanglement and the Sign Structure of Quantum States
- Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders
- The von Neumann entropy asymptotics in multidimensional fermionic systems
- Position momentum Duality in the Entanglement Spectrum of Free Fermions
- Entanglement Spheres and a UV-IR connection in Effective Field Theories
- Necessary and Sufficient Conditions for the Validity of Luttinger's Theorem
- Scattering and momentum space entanglement
- Momentum-space entanglement for interacting fermions at finite density
- Entanglement entropy and negativity in the Ising model with defects
- Divergences in open quantum systems
- Scaling theory for Mott-Hubbard transitions
- Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
- Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
- Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
- Momentum Space Entanglement from the Wilsonian Effective Action
- Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
- Wilsonian Effective Action and Entanglement Entropy
- Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
- Momentum space entanglement of interacting fermions
- Unveiling the Kondo cloud: unitary RG study of the Kondo model
- Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
- Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
- Origin of Topological Order in a Cooper Pair Insulator
- Holographic entanglement renormalisation of topological order in a quantum liquid
- Entanglement entropies and fermion signs of critical metals
- Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
- Momentum-space entanglement in scalar field theory on fuzzy spheres
- Frustration shapes multi-channel Kondo physics: a star graph perspective
- Exact Renormalization Group, Entanglement Entropy, and Black Hole Entropy
- Unveiling topological order through multipartite entanglement