The Hilbert-space structure of free fermions in disguise
arXiv:2507.15959 · doi:10.1088/1742-5468/ae29f5
Abstract
Free fermions in disguise (FFD) Hamiltonians describe spin chains which can be mapped to free fermions, but not via a Jordan-Wigner transformation. Although the mapping gives access to the full Hamiltonian spectrum, the computation of spin correlation functions is generally hard. Indeed, the dictionary between states in the spin and free-fermion Hilbert spaces is highly non-trivial, due to the non-linear and non-local nature of the mapping, as well as the exponential degeneracy of the Hamiltonian eigenspaces. In this work, we provide a series of results characterizing the Hilbert space associated to FFD Hamiltonians. We focus on the original model introduced by Paul Fendley and show that the corresponding Hilbert space admits the exact factorization , where hosts the fermionic operators, while accounts for the exponential degeneracy of the energy eigenspaces. By constructing a family of spin operators generating the operator algebra supported on , we further show that , where hosts ancillary free fermions in disguise, while is generated by the common eigenstates of an extensive set of commuting Pauli strings. Our construction allows us to fully resolve the exponential degeneracy of all Hamiltonian eigenspaces and is expected to have implications for the computation of spin correlation functions, both in and out of equilibrium.
arXiv comment14 pages, no figures; v4: minor revision
References in corpus (48)
- Anyons in an exactly solved model and beyond
- Time-dependence of correlation functions following a quantum quench
- Quantum Quench in the Transverse Field Ising Chain
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Form factors of the XXZ Heisenberg spin-1/2 finite chain
- Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
- Classical simulation of noninteracting-fermion quantum circuits
- An introduction to integrable techniques for one-dimensional quantum systems
- Mapping local Hamiltonians of fermions to local Hamiltonians of spins
- Circuit complexity for free fermions
- Generalized Jordan-Wigner Transformations
- Quantum circuits for strongly correlated quantum systems
- Quantum algorithms to simulate many-body physics of correlated fermions
- One-particle dynamical correlations in the one-dimensional Bose gas
- Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
- Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
- Fermionic Gaussian states: an introduction to numerical approaches
- Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
- Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
- On one-point functions for sinh-Gordon model at finite temperature
- Bose-Fermi Transformation In Three Dimensional Space
- Efficient classical simulation of matchgate circuits with generalized inputs and measurements
- Short distance correlators in the XXZ spin chain for arbitrary string distributions
- Free fermions in disguise
- Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
- Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
- Free fermionic and parafermionic quantum spin chains with multispin interactions
- From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
- Short-distance thermal correlations in the massive XXZ chain
- Fourier transform of fermionic systems and the spectral tensor network
- Free fermions behind the disguise
- Excited state correlations of the finite Heisenberg chain
- Characterization of solvable spin models via graph invariants
- Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
- Integrable quantum spin chains with free fermionic and parafermionic spectrum
- Exact formulas for the form factors of local operators in the Lieb-Liniger model
- Particle exchange statistics beyond fermions and bosons
- Cooper pairs and exclusion statistics from coupled free-fermion chains
- Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
- Jordan-Wigner transformations for tree structures
- Geometric Criterion for Solvability of Lattice Spin Systems
- Exact solution of a cluster model with next-nearest-neighbor interaction
- Free fermions beyond Jordan and Wigner
- Quantum circuits with free fermions in disguise
- A curious mapping between supersymmetric quantum chains
- Exact real time dynamics with free fermions in disguise