Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2105.04326

A Spin $1/2$ Fermions Chain with $XY$ Interaction

Gianluca Francica

Published May 10, 2021• 0 citations
arXivHTMLPDF

Abstract

We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a $XY$ antiferromagnetic interaction. The $XY$ term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.

DOI
10.48550/arxiv.2105.04326

Related papers

Exact Solution for the Interacting Kitaev Chain at the Symmetric Point

Jian-Jian Miao, Hui-Ke Jin, Fu‐Chun Zhang +1 more

The Kitaev chain model with a nearest neighbor interaction U is solved exactly at the symmetry point Δ=t and chemical potential μ=0 in an open boundary condition. By applying two Jordan-Wigner transformations and a spin rotation, such a symmetric interacting model is mapped onto a noninteracting fermion model, which can be diagonalized exactly. The solutions include a topologically nontrivial phase at |U|<t and a topologically trivial phase at |U|>t. The two phases are related by dualities. Quantum phase transitions in the model are studied with the help of the exact solution.

arXiv:1610.04485•Physical Review Letters•Jun 27, 2017•76 citations

Coexistence of strong and weak Majorana zero modes in an anisotropic XY spin chain with second-neighbor interactions

Kazuhiro Wada, Takanori Sugimoto, Takami Tohyama

We theoretically investigate Majorana zero modes emerging in an anisotropic XY spin chain with second-neighbor interactions. The spin chain is mathematically equivalent to the Kitaev chain comprised of spinless fermions if only nearest-neighbor interactions are considered. Recent studies on the Kitaev chain with long-ranged interactions, have presented coexistence of several Majorana zero modes. Investigating the topological phase diagram of the anisotropic XY spin chain with second-neighbor interactions, we find coexistence of several Majorana zero modes similar to the Kitaev chain. However, we confirm that one of the zero modes is restricted into a Hilbert subspace. The mode is regarded as a so-called weak zero mode that should exhibit thermodynamical properties different from a (strong) zero mode appearing in the whole Hilbert space. Since the quantum statistics of spin is the same as a hard-core boson, we expect an experimental realization of the weak mode in not only quantum spin materials but also optical lattices for cold atom systems.

arXiv:2103.12281•Physical review. B./Physical review. B•Aug 12, 2021•13 citations

Quantum phases of spin-1/2 extended XY model in transverse magnetic field

Rakesh Kumar Malakar, Asim Kumar Ghosh

Abstract In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but Z 2 symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan-Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.

arXiv:2310.11243•Physica Scripta•Jan 31, 2024•5 citations

Pairing in spinless fermions and spin chains with next-nearest neighbor interactions

Lorenzo Gotta, Leonardo Mazza, Pascal Simon +1 more

We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions.Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations.The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles.In relation with recent studies, we show several emergent transition lines with a central charge c = 3/2 between the Luttinger liquid and the cluster Luttinger liquid phases.These results could be experimentally investigated using highly tunable quantum simulators.

arXiv:2006.07128•Physical Review Research•Feb 8, 2021•15 citations

Exact weak bosonic zero modes in a spin/fermion chain

Jianlong Fu

We study an exactly solvable one-dimensional spin-$\frac{1}{2}$ model which can support weak zero modes in its ground-state manifold. The spin chain has staggered $XXZ$-type and $ZZ$-type spin interaction on neighboring bonds and is thus dubbed the ($XXZ,Z$) chain. The model is equivalent to an interacting fermionic chain by Jordan-Wigner transformation. We study the phase diagram of the system and work out the conditions and properties of its weak zero modes. In the fermion chain representation, these weak zero modes are given by even-order polynomials of Majorana fermion operators and are thus bosonic. The fermionic chain Hamiltonian contains only fermion hopping and interaction terms and may have potential realization in experiments.

arXiv:2112.12824•Physical review. B./Physical review. B•Oct 28, 2022•5 citations

Exact Solution for an Interacting Spin One-Half Chain at the Symmetric Point

Gianluca Francica, Paola Gentile, Mario Cuoco

The p-wave superconductive wire with Hubbard interaction $U$ is solved exactly at the symmetry point $\Delta=t$ and chemical potential $\mu=0$ in an open boundary condition. By applying two Jordan-Wigner transformations and individuating non-local constant of motions such interacting model is mapped onto a noninteracting fermion model which can be diagonalized exactly. In the lowest energy subspace the mapping is onto a Kitaev chain. The system enters in a topologically trivial phase due to a second order quantum phase transition at $U=\pm 2t$. The features of the quantum phases are characterized with the help of the exact solution.

arXiv:1905.11090•May 27, 2019•0 citations
A Spin 1/21/21/2 Fermions Chain with XYXYXY Interaction
We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a XYXYXY antiferromagnetic interaction. The XYXYXY term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.
The Kitaev chain model with a nearest neighbor interaction U is solved exactly at the symmetry point Δ=t and chemical potential μ=0 in an open boundary condition. By applying two Jordan-Wigner transformations and a spin rotation, such a symmetric interacting model is mapped onto a noninteracting fermion model, which can be diagonalized exactly. The solutions include a topologically nontrivial phase at |U|<t and a topologically trivial phase at |U|>t. The two phases are related by dualities. Quantum phase transitions in the model are studied with the help of the exact solution.
We theoretically investigate Majorana zero modes emerging in an anisotropic XY spin chain with second-neighbor interactions. The spin chain is mathematically equivalent to the Kitaev chain comprised of spinless fermions if only nearest-neighbor interactions are considered. Recent studies on the Kitaev chain with long-ranged interactions, have presented coexistence of several Majorana zero modes. Investigating the topological phase diagram of the anisotropic XY spin chain with second-neighbor interactions, we find coexistence of several Majorana zero modes similar to the Kitaev chain. However, we confirm that one of the zero modes is restricted into a Hilbert subspace. The mode is regarded as a so-called weak zero mode that should exhibit thermodynamical properties different from a (strong) zero mode appearing in the whole Hilbert space. Since the quantum statistics of spin is the same as a hard-core boson, we expect an experimental realization of the weak mode in not only quantum spin materials but also optical lattices for cold atom systems.
Abstract In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but Z 2 symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan-Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions.Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations.The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles.In relation with recent studies, we show several emergent transition lines with a central charge c = 3/2 between the Luttinger liquid and the cluster Luttinger liquid phases.These results could be experimentally investigated using highly tunable quantum simulators.
We study an exactly solvable one-dimensional spin-12\frac{1}{2}21​ model which can support weak zero modes in its ground-state manifold. The spin chain has staggered XXZXXZXXZ-type and ZZZZZZ-type spin interaction on neighboring bonds and is thus dubbed the (XXZ,ZXXZ,ZXXZ,Z) chain. The model is equivalent to an interacting fermionic chain by Jordan-Wigner transformation. We study the phase diagram of the system and work out the conditions and properties of its weak zero modes. In the fermion chain representation, these weak zero modes are given by even-order polynomials of Majorana fermion operators and are thus bosonic. The fermionic chain Hamiltonian contains only fermion hopping and interaction terms and may have potential realization in experiments.
The p-wave superconductive wire with Hubbard interaction UUU is solved exactly at the symmetry point Δ=t\Delta=tΔ=t and chemical potential μ=0\mu=0μ=0 in an open boundary condition. By applying two Jordan-Wigner transformations and individuating non-local constant of motions such interacting model is mapped onto a noninteracting fermion model which can be diagonalized exactly. In the lowest energy subspace the mapping is onto a Kitaev chain. The system enters in a topologically trivial phase due to a second order quantum phase transition at U=±2tU=\pm 2tU=±2t. The features of the quantum phases are characterized with the help of the exact solution.