What is the topological dual of the XXZ spin Chain?

• URL: http://arxiv.org/abs/2507.22119v1
• Date: Tue, 29 Jul 2025 18:00:03 GMT
• Title: What is the topological dual of the XXZ spin Chain?
• Abstract summary: We construct a dual symmetry-protected topological (SPT) Hamiltonian for the $U(1)$ symmetric anisotropic spin-$frac12$ Heisenberg chain-a model.<n>By performing a non-local unitary transformation, we explicitly construct a local fermionic Hamiltonian that exhibits two nontrivial topological phases separated by an extended Luttinger liquid regime.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We construct a dual symmetry-protected topological (SPT) Hamiltonian for the $U(1)$ symmetric anisotropic spin-$\frac{1}{2}$ Heisenberg chain-a model that has traditionally been used to study spontaneous symmetry breaking (SSB) in both ferromagnetic and antiferromagnetic phases, with an intervening extended Luttinger liquid phase. By performing a non-local unitary transformation, we explicitly construct a local fermionic Hamiltonian that exhibits two nontrivial topological phases separated by an extended Luttinger liquid regime. We demonstrate the topological nature of these phases by analyzing the entanglement structure, deriving a non-local string order parameter, and constructing an exact zero mode operator that connects states in different fermionic parity sectors.

Related papers

• Geometric Phases in Two-Level Mixing: From Neutral Mesons to Holonomic Qubits and Topological Majorana Modes [1.5675763601034223]
  We investigate a Hermitian two-level mixing Hamiltonian motivated by neutral meson oscillations and its connections with qubit, fermionic, and topological descriptions.
  arXiv  Detail & Related papers  (2026-09-06T22:10:48Z)
• Topological properties and Majorana Multiplicity in Zigzag Kitaev Chain [0.9857968274865204]
  We investigate the spectral and topological properties of a zigzag Kitaev chain constructed from two diagonally coupled one dimensional Kitaev chains with a zero and finite superconducting pairing phase difference.<n>For a zero phase difference, the resulting energy spectrum shows topological phases with two, four MZMs, and trivial regions.<n>Our results establish the zigzag Kitaev chain as a minimal platform for engineering MZM quantum computations, with potential applications in the study of topological phases and Majorana based qubit physics.
  arXiv  Detail & Related papers  (2026-07-05T16:47:29Z)
• Mixed-State Topological Phase: Quantized Topological Order Parameter and Lieb-Schultz-Mattis Theorem [7.727969651316747]
  We investigate the extension of pure-state symmetry protected topological phases to mixed-state regime with a strong U(1) and a weak $mathbbZ$ symmetries in one-dimensional spin systems.<n>We propose a corresponding topological phase order parameter for short-range entangled mixed states by showing that it is quantized and its distinct values can be realized by concrete spin systems with disorders.
  arXiv  Detail & Related papers  (2026-03-25T07:46:05Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Emergence of a Luttinger Liquid Phase in an Array of Chiral Molecules [0.0]
  We propose a robust platform for simulating chiral quantum magnetism using linear arrays of trapped asymmetric top molecules.<n>By mapping the Stark-dressed rotational states onto an effective spin-$1/2$ subspace, we rigorously derive a generalized $XXZ$ Heisenberg Hamiltonian governing the underlying many-body dynamics.<n>Our results establish 1,2-propanediol arrays as a versatile quantum simulator, providing a direct microscopic link between molecular chirality and topological many-body phases.
  arXiv  Detail & Related papers  (2026-02-10T17:23:36Z)
• Symmetry and Topology in the Non-Hermitian Kitaev chain [1.4273866043218153]
  We study the non-Hermitian Kitaev chain with non-reciprocal hopping amplitudes and asymmetric superconducting pairing.<n>We show that particle-hole symmetry (PHS) is preserved throughout the entire parameter regime.<n>We present the topological phase diagram of the non-Hermitian Kitaev chain across a broad range of complex parameters.
  arXiv  Detail & Related papers  (2026-01-02T19:00:02Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction.<n>Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup [0.6675805308519986]
  Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. In this work, we study an emergent $mathbbZ$-gauged system with global $U(1)$. We also discuss the stability of these phases and the critical points to small perturbations and their potential experimental realizations.
  arXiv  Detail & Related papers  (2024-01-22T05:46:49Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Symmetry-protected topological corner modes in a periodically driven interacting spin lattice [0.0]
  Floquet symmetry protected second-order topological phases in a simple but insightful two-dimensional spin-1/2 lattice. We show that corner localized $mathbbZ$ symmetry broken operators commute and anticommute with the one-period time evolution operator. We propose a means to detect the signature of such modes in experiments and discuss the effect of imperfections.
  arXiv  Detail & Related papers  (2022-06-14T07:51:20Z)
• Spin-spin coupling-based quantum and classical phase transitions in two-impurity spin-boson models [55.41644538483948]
  Two-interacting-impurity spin-boson models with vanishing transverse fields on the spin-pair are studied. The dynamics of the magnetization is analysed for different levels of (an)isotropy.
  arXiv  Detail & Related papers  (2022-05-19T08:01:03Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite [50.591267188664666]
  We reveal a rich ground state phase diagram even at the classical level. The presented model opens a new direction in the study of kagome antiferromagnets.
  arXiv  Detail & Related papers  (2021-07-28T18:00:03Z)
• Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model [0.0]
  We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase.
  arXiv  Detail & Related papers  (2020-10-01T01:20:46Z)
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder [0.0]
  Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical and transport properties. We introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.
  arXiv  Detail & Related papers  (2020-06-16T03:22:53Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.