Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

Abstract

We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological $\Theta$-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological $\Theta$-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.

arXiv comment51 pages, 14 figures, 126 references

References in corpus (64)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Classification of topological quantum matter with symmetries
• Entanglement in quantum critical phenomena
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Aspects of Holographic Entanglement Entropy
• Geometric and Renormalized Entropy in Conformal Field Theory
• Towards a derivation of holographic entanglement entropy
• Renormalization Group Approach to Interacting Fermions
• Entanglement spectrum of a topological phase in one dimension
• Entanglement renormalization
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Entanglement Renormalization and Holography
• Classifying quantum phases using Matrix Product States and PEPS
• Functional renormalization group approach to correlated fermion systems
• Holography from Conformal Field Theory
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• On the Holographic Renormalization Group
• Tensor networks for complex quantum systems
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Violation of the entropic area law for Fermions
• Holographic and Wilsonian Renormalization Groups
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
• Quantum Noise as an Entanglement Meter
• Single particle Green's functions and interacting topological insulators
• Algorithms for entanglement renormalization
• Polarization and localization in insulators: generating function approach
• Superconductors are topologically ordered
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Entanglement and alpha entropies for a massive Dirac field in two dimensions
• Entanglement in XY Spin Chain
• Spacetime and the Holographic Renormalization Group
• Tensor network states and geometry
• Entanglement Entropy and the Fermi Surface
• Non-perturbative approach to Luttinger's theorem in one dimension
• Explicit Local Integrals of Motion for the Many-Body Localized State
• Low energy effective Hamiltonian for the XXZ spin chain
• Fermionic multi-scale entanglement renormalization ansatz
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• A numerical canonical transformation approach to quantum many body problems
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Quantum Renormalization Group and Holography
• Topological phase in one-dimensional interacting fermion system
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
• Many-body localization and delocalization from the perspective of Integrals of Motion
• Holographic description of quantum field theory
• Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains
• Symmetry protected topological phases of 1D interacting fermions with spin-charge separation
• Universality, marginal operators, and limit cycles
• Exact holographic mapping in free fermion systems
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Horizon as Critical Phenomenon
• Extracting entanglement geometry from quantum states
• Spontaneous Symmetry Breaking and Decoherence in Superconductors
• Haldane Gap and Fractional Oscillations in Gated Josephson Arrays
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• One-dimensional fermions with incommensuration
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality

Cited by in corpus (8)

• Unveiling the Kondo cloud: unitary RG study of the Kondo model
• Holographic entanglement renormalisation of topological order in a quantum liquid
• Origin of Topological Order in a Cooper Pair Insulator
• Frustration shapes multi-channel Kondo physics: a star graph perspective
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Kondo frustration via charge fluctuations: a route to Mott localisation
• Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal
• Unveiling topological order through multipartite entanglement