The fidelity approach to the Hubbard model

Abstract

We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero.

8 pages, 4 figures, added results on the hyper-scaling form of the fidelity metric

References in corpus (17)

• One-Dimensional Fermi liquids
• Ground state overlap and quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Quantum fidelity and quantum phase transitions in matrix product states
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Ground-state fidelity in one-dimensional gapless model
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension
• Ground state fidelity and quantum phase transitions in free Fermi systems
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Finite Size Scaling of the Spin Stiffness of the Antiferromagnetic S=1/2 XXZ chain

Cited by in corpus (40)

• Fidelity approach to quantum phase transitions
• Quantum enhanced measurements without entanglement
• Quantum Critical Scaling of Fidelity Susceptibility
• Geometry of quantum phase transitions
• Loschmidt Echo for quantum metrology
• On quantumness in multi-parameter quantum estimation
• Interaction effects and quantum phase transitions in topological insulators
• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
• Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• Oscillating fidelity susceptibility near a quantum multicritical point
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
• Fidelity and superconductivity in two-dimensional t-J models
• Quantum phases of hard-core bosons in a frustrated honeycomb lattice
• A Fidelity Study of the Superconducting Phase Diagram in the 2D Single-band Hubbard Model
• Loschmidt echo in the Bose-Hubbard model: turning back time in an optical lattice
• Entanglement modes and topological phase transitions in superconductors
• Ground-state properties of the one-dimensional attractive Hubbard model with confinement: a comparative study
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Thermal states of the Kitaev honeycomb model: a Bures metric analysis
• Analytical and numerical studies of the one-dimensional sawtooth chain
• Fidelity Study of Superconductivity in Extended Hubbard Models
• Density-functional fidelity approach to quantum phase transitions
• Challenges and constraints of dynamically emerged source and sink in atomtronic circuits: From closed-system to open-system approaches
• Mesoscopic Effects in Quantum Phases of Ultracold Quantum Gases in Optical Lattices
• Criticality in the Bose-Hubbard model with three-body repulsion
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Site-wise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators
• Quantum spin liquids of Rydberg excitations in a honeycomb lattice induced by density-dependent Peierls phases
• Lieb's Theorem and Maximum Entropy Condensates
• Phase transitions, entanglement and quantum noise interferometry in cold atoms
• Reduced fidelity approach for quantum phase transitions in spin-1/2 dimerized Heisenberg chains
• Vanishing k-space fidelity and phase diagram's bulk-edge-bulk correspondence
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model
• Nonequilibrium quantum dynamics of partial symmetry breaking for ultracold bosons in an optical lattice ring trap
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux