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:1911.03156 · Physical review. B./Physical review. B

Study of the phase diagram of the Kitaev-Hubbard chain

Iman Mahyaeh, Eddy Ardonne

Published Feb 14, 2020• 26 citations
arXivHTMLPDF

Abstract

We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbor density-density interaction, using both analytical techniques as well as DMRG. In the case of a moderate attractive interaction, the model has the same phases as the noninteracting chain, a trivial and a topological phase. For repulsive interactions, the phase diagram is more interesting. Apart from the previously observed topological, incommensurate, and charge density wave phases, we identify the ``excited state charge density wave'' phase. In this phase, the ground state resembles an excited state of an ordinary charge density phase, but is lower in energy due to the frustrated nature of the model. We find that the dynamical critical exponent takes the value $z\ensuremath{\simeq}1.8$. Interestingly, this phase only appears for even system sizes, and is sensitive to the chemical potential on the edges of the chain. For the topological phase, we present an argument that excludes the presence of a strong zero mode for a large part of the topological phase. For the remaining region, we study the time dependence of the edge magnetization (using the bosonic incarnation of the model). These results further expand the region where a strong zero mode does not occur.

DOI
10.1103/physrevb.101.085125

Related papers

Phase diagram and entanglement of two interacting topological Kitaev chains

Loïc Herviou, Christophe Mora, Karyn Le Hur

A superconducting wire described by a $p$-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.

arXiv:1601.02998•Physical review. B./Physical review. B•Apr 27, 2016•21 citations

Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder

Kevin S.C. Decker, Christoph Karrasch

Abstract We document the ground state phase diagram of the one-dimensional Kitaev chain with quasi-periodic disorder in the presence of two-body interactions. Our data were obtained for systems of $$L=1000$$ L = 1000 sites using large-scale density-matrix renormalization group numerics and is benchmarked against known results for the clean system. We demonstrate that moderate quasi-periodic disorder stabilizes the topological phase both for repulsive and attractive interactions. For larger disorder strengths, the system features re-entrance behavior and multiple phase transitions. Graphical abstract Phase diagram as a function of the chemical potential and the disorder strength for repulsive interactions

arXiv:2402.12897•The European Physical Journal B•Aug 1, 2024•3 citations

Topological Phase Diagram of an Interacting Kitaev Chain: Mean Field versus DMRG Study

Giovanni Nunziante, Alfonso Maiellaro, Claudio Guarcello +1 more

In this work, we study the topological phase transitions of a Kitaev chain generalized by the addition of nearest-neighbor Coulomb interaction. We show the presence of a robust topological phase as a function of the interaction strength and of the on-site energy with associated non-zero energy Majorana states localized at the chain edges. We provide an effective mean-field model that allows for the self-consistent computation of the mean value of the local particle number operator, and we also perform Density Matrix Renormalization Group numerical simulations based on a tensor network approach. We find that the two methods show a good agreement in reporting the phase transition between trivial and topological superconductivity. Temperature robustness within a physically relevant threshold has also been demonstrated. These findings shed light on an entire class of topological interacting one-dimensional systems in which the effects of residual Coulomb interactions play a relevant role.

Condensed Matter•Mar 20, 2024•0 citations

Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study

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

We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalization-group method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.

arXiv:1608.08382•Scientific Reports•Jan 5, 2018•25 citations

Field theory of competing phases in the interacting Kitaev chain

Pradip Kattel, Thierry Giamarchi

We study the interacting Kitaev chain with nearest-neighbor interactions and finite chemical potential using a combination of bosonization and density-matrix renormalization-group calculations. Focusing away from special exactly solvable lattice limits, we develop a continuum field-theoretic description of the generic finite-density interacting regime, where doping nonperturbatively modifies the competition between superconducting pairing and commensurate charge ordering. We show that the phase diagram consists of an intermediate incommensurate Luttinger liquid between the topological superconducting and commensurate charge-density-wave Mott phases, as well as a trivial band-insulating regime at large chemical potential. The commensurate--incommensurate and incommensurate--topological-superconducting phase boundaries are governed by Pokrovsky--Talapov and Berezinskii--Kosterlitz--Thouless criticality, respectively. We analyze the interacting topological superconducting regime and its boundary excitations. At the semiclassical level, and explicitly in the free-fermion boundary theory, the topological phase supports exponentially localized Majorana edge modes at interfaces between topological and trivial regions. We also construct a dual continuum fermionic representation in which this topological bulk sector is described instead by conventional symmetry breaking. This gives a continuum version of the SPT--SSB correspondence between different fermionic representations. Overall, our results provide an analytical description of one-dimensional interacting topological superconductors, from the competition between topology and commensurability and the resulting quantum criticality to the dual symmetry-breaking description of the topological phase.

arXiv:2610.37761•Oct 27, 2026•0 citations

One-dimensional Bose-Hubbard model with nearest-neighbor interaction

Till D. Kühner, Steven R. White, H. Monien

We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.

arXiv:cond-mat/9906019•Physical review. B, Condensed matter•May 1, 2000•401 citations
We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbor density-density interaction, using both analytical techniques as well as DMRG. In the case of a moderate attractive interaction, the model has the same phases as the noninteracting chain, a trivial and a topological phase. For repulsive interactions, the phase diagram is more interesting. Apart from the previously observed topological, incommensurate, and charge density wave phases, we identify the ``excited state charge density wave'' phase. In this phase, the ground state resembles an excited state of an ordinary charge density phase, but is lower in energy due to the frustrated nature of the model. We find that the dynamical critical exponent takes the value z\ensuremath≃1.8z\ensuremath{\simeq}1.8z\ensuremath≃1.8. Interestingly, this phase only appears for even system sizes, and is sensitive to the chemical potential on the edges of the chain. For the topological phase, we present an argument that excludes the presence of a strong zero mode for a large part of the topological phase. For the remaining region, we study the time dependence of the edge magnetization (using the bosonic incarnation of the model). These results further expand the region where a strong zero mode does not occur.
A superconducting wire described by a ppp-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.
Abstract We document the ground state phase diagram of the one-dimensional Kitaev chain with quasi-periodic disorder in the presence of two-body interactions. Our data were obtained for systems of L=1000L=1000L=1000 L = 1000 sites using large-scale density-matrix renormalization group numerics and is benchmarked against known results for the clean system. We demonstrate that moderate quasi-periodic disorder stabilizes the topological phase both for repulsive and attractive interactions. For larger disorder strengths, the system features re-entrance behavior and multiple phase transitions. Graphical abstract Phase diagram as a function of the chemical potential and the disorder strength for repulsive interactions
In this work, we study the topological phase transitions of a Kitaev chain generalized by the addition of nearest-neighbor Coulomb interaction. We show the presence of a robust topological phase as a function of the interaction strength and of the on-site energy with associated non-zero energy Majorana states localized at the chain edges. We provide an effective mean-field model that allows for the self-consistent computation of the mean value of the local particle number operator, and we also perform Density Matrix Renormalization Group numerical simulations based on a tensor network approach. We find that the two methods show a good agreement in reporting the phase transition between trivial and topological superconductivity. Temperature robustness within a physically relevant threshold has also been demonstrated. These findings shed light on an entire class of topological interacting one-dimensional systems in which the effects of residual Coulomb interactions play a relevant role.
We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalization-group method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.
We study the interacting Kitaev chain with nearest-neighbor interactions and finite chemical potential using a combination of bosonization and density-matrix renormalization-group calculations. Focusing away from special exactly solvable lattice limits, we develop a continuum field-theoretic description of the generic finite-density interacting regime, where doping nonperturbatively modifies the competition between superconducting pairing and commensurate charge ordering. We show that the phase diagram consists of an intermediate incommensurate Luttinger liquid between the topological superconducting and commensurate charge-density-wave Mott phases, as well as a trivial band-insulating regime at large chemical potential. The commensurate--incommensurate and incommensurate--topological-superconducting phase boundaries are governed by Pokrovsky--Talapov and Berezinskii--Kosterlitz--Thouless criticality, respectively. We analyze the interacting topological superconducting regime and its boundary excitations. At the semiclassical level, and explicitly in the free-fermion boundary theory, the topological phase supports exponentially localized Majorana edge modes at interfaces between topological and trivial regions. We also construct a dual continuum fermionic representation in which this topological bulk sector is described instead by conventional symmetry breaking. This gives a continuum version of the SPT--SSB correspondence between different fermionic representations. Overall, our results provide an analytical description of one-dimensional interacting topological superconductors, from the competition between topology and commensurability and the resulting quantum criticality to the dual symmetry-breaking description of the topological phase.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.