The deformed Inozemtsev spin chain

Abstract

The Inozemtsev chain is an exactly solvable interpolation between the short-range Heisenberg and long-range Haldane-Shastry (HS) chains. In order to unlock its potential to study spin interactions with tunable interaction range using the powerful tools of integrability, the model's mathematical properties require better understanding. As a major step in this direction, we present a new generalisation of the Inozemtsev chain with spin symmetry reduced to U(1), interpolating between a Heisenberg xxz chain and the xxz-type HS chain, and integrable throughout. Underlying it is a new quantum many-body system that extends the elliptic Ruijsenaars system by including spins, contains the trigonometric spin-Ruijsenaars-Macdonald system as a special case, and yields our spin chain by 'freezing'. Our models have potential applications from condensed-matter to high-energy theory, and provide a crucial step towards a general theory for long-range integrability.

v1: 8 pages, 1 figure; v2-3: minor changes; v4: 6+7 pages, substantial changes, introduction and supplemental material expanded; v5: 25 pages, 2 figures, restructured, minor changes

References in corpus (42)

• Trapped-Ion Quantum Computing: Progress and Challenges
• Observation of a Discrete Time Crystal
• Observation of entanglement propagation in a quantum many-body system
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Experimental Comparison of Two Quantum Computing Architectures
• Spread of correlations in long-range interacting quantum systems
• Long-range interacting quantum systems
• Yang-Baxter equation in spin chains with long range interactions
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Lattice Integrable Systems of Haldane-Shastry Type
• The Blob Algebra and the Periodic Temperley-Lieb Algebra
• On an algebraic approach to higher dimensional statistical mechanics
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Spinons in Conformal Field Theory
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
• Integrals of motion of the Haldane Shastry Model
• Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
• Elliptic quantum groups and Ruijsenaars models
• The Quantum DELL System
• Resurrecting the partially isotropic Haldane-Shastry model
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• The trigonometric counterpart of the Haldane Shastry Model
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials
• On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories
• Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model
• Hypergeometric theta functions and elliptic Macdonald polynomials
• Construction of eigenfunctions for the elliptic Ruijsenaars difference operators
• Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Wrapping corrections for long range spin chains
• From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
• Cladistics of Double Yangians and Elliptic Algebras
• Trapped-ion quantum simulation of tunable-range Heisenberg chains
• On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange
• Lifting integrable models and long-range interactions
• The Commutativity of Integrals of Motion for Quantum Spin Chains and Elliptic Functions Identities
• Integrability of the Inozemtsev spin chain

Cited by in corpus (2)

• Quantum group deformation of the Kittel--Shore model
• A solvable non-unitary fermionic long-range model with extended symmetry