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:2604.24068

Ground state of the Hubbard model with spin-dependent linear potential

Jacek Dobrzyniecki, Thomas Busch

Published Apr 27, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a linear external potential whose gradient is opposite for the two spin components, so that each spin species sees a potential minimum at a different end of the lattice. Using density-matrix renormalization group (DMRG) simulations, we map the ground-state density distributions and the number of doubly occupied sites as a function of the potential gradient $β$ and interaction strength. We identify three distinct regimes separated by critical threshold gradients: (i) a small-$β$ regime where fermion pairing remains robust against the external potential; (ii) an intermediate-$β$ phase-separated regime characterized by a staircase-like decrease in the doublon number, corresponding to the successive, one-by-one breaking of bound pairs; and (iii) a large-$β$ regime where the two spin components are completely spatially separated. We complement the numerical results with a phenomenological model and a local-density approximation analysis, from which we derive closed-form analytical estimates for these critical threshold values. We also verify that the staircase structure persists under additional harmonic confinement. Our results are directly testable in cold-atom experiments, and demonstrate that a spin-dependent linear potential enables precise, integer-level control of the number of bound fermion pairs.

DOI
10.48550/arxiv.2604.24068

Related papers

Phase diagram of the Fermi–Hubbard model with spin-dependent external potentials: A DMRG study

Xingbo Wei, Ye-Ming Meng, Zhe‐Ming Wu +1 more

We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin-dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, a normal polarized phase, and a Bardeen–Cooper–Schrieffer (BCS) phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.

Chinese Physics B•Nov 1, 2015•3 citations

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory

Gao Xianlong

We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the intercomponents. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.

arXiv:1309.5198•Physical Review A•Feb 26, 2013•7 citations

Phase-separated ferromagnetism in a spin-imbalanced system of Fermi atoms loaded in an optical ladder: A density-matrix renormalization-group study

Masahiko Okumura, S. Yamada, Masahiko Machida +1 more

We consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction $U$ and spin imbalance $p$ in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough $U$ and $p$. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.

arXiv:1008.3055•Physical Review A•Mar 9, 2011•16 citations

Ground and excited-state fermions in a one-dimensional double-well: Exact and density-functional solutions

Rudolph J Magyar

Two of the most popular quantum-mechanical models of interacting fermions are compared to each other and to potentially exact solutions for a pair of contact-interacting fermions trapped in a one-dimensional (1D) double-well potential, a model of atoms in a quasi-1D optical lattice, or electrons of a hydrogen molecule in a strong magnetic field. An exact few-body Hamiltonian is solved numerically in momentum space yielding a highly correlated eigenspectrum. Additionally, approximate ground-state energies are obtained using both density-functional theory (DFT) functional and two-site Hubbard models. A 1D adiabatic local-density approximation kernel is constructed for use in time-dependent density-functional theory (TDDFT) and the resulting excited-state spectrum is compared to the exact and Hubbard results. DFT is shown to give accurate results for wells with small separations but fails to describe localization of opposite spin fermions to different sites. A locally cognizant density functional based on an effective local fermion number would provide a solution to this problem, and an approximate treatment presented here compares favorably to the exact and Hubbard results. The TDDFT excited-state spectrum is accurate in the small parameter regime with nonadiabatic effects accounting for any deviations. As expected, the ground-state Hubbard model outperforms DFT at large separations but breaks down at intermediate separations due to improper scaling to the united-atom limit. At strong coupling, both Hubbard and TDDFT methods fail to capture the appropriate energetics.

Physical Review B•May 26, 2009•16 citations

Ground-state properties of the one-dimensional attractive Hubbard model with confinement: A comparative study

Ji-Hong Hu, Jingjing Wang, Gao Xianlong +4 more

We revisit the one-dimensional attractive Hubbard model by using the Bethe-ansatz-based density-functional theory and density-matrix renormalization method. The ground-state properties of this model are discussed in details for different fillings and different confining conditions in weak-to-intermediate coupling regime. We investigate the ground-state energy, energy gap, and pair-binding energy and compare them with those calculated from the canonical Bardeen-Cooper-Schrieffer approximation. We find that the Bethe-ansatz-based density-functional theory is computationally easy and yields an accurate description of the ground-state properties for weak-to-intermediate interaction strength, different fillings, and confinements. In order to characterize the quantum phase transition in the presence of a harmonic confinement, we calculate the thermodynamic stiffness, the density-functional fidelity, and fidelity susceptibility, respectively. It is shown that with the increase in the number of particles or attractive interaction strength, the system can be driven from the Luther-Emery-type phase to the composite phase of Luther-Emery-type in the wings and insulatinglike in the center.

arXiv:1101.0962•Physical Review B•Jul 14, 2010•20 citations

Phase separation of trapped spin-imbalanced Fermi gases in one-dimensional optical lattices

Fabian Heidrich‐Meisner, Giuliano Orso, Adrian E. Feiguin

We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local-density approximation (LDA) and density-matrix renormalization-group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, the LDA predicts that the gas phase separates into shells with a partially polarized core and fully paired wings, the latter occurring below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. We show that, unlike in the continuum case, the critical polarization is a nonmonotonic function of the interaction strength and vanishes in the limit of large interactions.

arXiv:1001.4720•Physical Review A•May 6, 2010•49 citations
We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a linear external potential whose gradient is opposite for the two spin components, so that each spin species sees a potential minimum at a different end of the lattice. Using density-matrix renormalization group (DMRG) simulations, we map the ground-state density distributions and the number of doubly occupied sites as a function of the potential gradient βββ and interaction strength. We identify three distinct regimes separated by critical threshold gradients: (i) a small-βββ regime where fermion pairing remains robust against the external potential; (ii) an intermediate-βββ phase-separated regime characterized by a staircase-like decrease in the doublon number, corresponding to the successive, one-by-one breaking of bound pairs; and (iii) a large-βββ regime where the two spin components are completely spatially separated. We complement the numerical results with a phenomenological model and a local-density approximation analysis, from which we derive closed-form analytical estimates for these critical threshold values. We also verify that the staircase structure persists under additional harmonic confinement. Our results are directly testable in cold-atom experiments, and demonstrate that a spin-dependent linear potential enables precise, integer-level control of the number of bound fermion pairs.
We investigate a one-dimensional two-component system in an optical lattice of attractive interactions under a spin-dependent external potential. Based on the density-matrix renormalization group methods, we obtain its phase diagram as a function of the external potential imbalance and the strength of the attractive interaction through the analysis on the density profiles and the momentum pair correlation functions. We find that there are three different phases in the system, a coexisted fully polarized and Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase, a normal polarized phase, and a Bardeen–Cooper–Schrieffer (BCS) phase. Different from the systems of spin-independent external potential, where the FFLO phase is normally favored by the attractive interactions, in the present situation, the FFLO phases are easily destroyed by the attractive interactions, leading to the normal polarized or the BCS phase.
We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the intercomponents. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.
We consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction UUU and spin imbalance ppp in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough UUU and ppp. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.
Two of the most popular quantum-mechanical models of interacting fermions are compared to each other and to potentially exact solutions for a pair of contact-interacting fermions trapped in a one-dimensional (1D) double-well potential, a model of atoms in a quasi-1D optical lattice, or electrons of a hydrogen molecule in a strong magnetic field. An exact few-body Hamiltonian is solved numerically in momentum space yielding a highly correlated eigenspectrum. Additionally, approximate ground-state energies are obtained using both density-functional theory (DFT) functional and two-site Hubbard models. A 1D adiabatic local-density approximation kernel is constructed for use in time-dependent density-functional theory (TDDFT) and the resulting excited-state spectrum is compared to the exact and Hubbard results. DFT is shown to give accurate results for wells with small separations but fails to describe localization of opposite spin fermions to different sites. A locally cognizant density functional based on an effective local fermion number would provide a solution to this problem, and an approximate treatment presented here compares favorably to the exact and Hubbard results. The TDDFT excited-state spectrum is accurate in the small parameter regime with nonadiabatic effects accounting for any deviations. As expected, the ground-state Hubbard model outperforms DFT at large separations but breaks down at intermediate separations due to improper scaling to the united-atom limit. At strong coupling, both Hubbard and TDDFT methods fail to capture the appropriate energetics.
We revisit the one-dimensional attractive Hubbard model by using the Bethe-ansatz-based density-functional theory and density-matrix renormalization method. The ground-state properties of this model are discussed in details for different fillings and different confining conditions in weak-to-intermediate coupling regime. We investigate the ground-state energy, energy gap, and pair-binding energy and compare them with those calculated from the canonical Bardeen-Cooper-Schrieffer approximation. We find that the Bethe-ansatz-based density-functional theory is computationally easy and yields an accurate description of the ground-state properties for weak-to-intermediate interaction strength, different fillings, and confinements. In order to characterize the quantum phase transition in the presence of a harmonic confinement, we calculate the thermodynamic stiffness, the density-functional fidelity, and fidelity susceptibility, respectively. It is shown that with the increase in the number of particles or attractive interaction strength, the system can be driven from the Luther-Emery-type phase to the composite phase of Luther-Emery-type in the wings and insulatinglike in the center.
We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local-density approximation (LDA) and density-matrix renormalization-group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, the LDA predicts that the gas phase separates into shells with a partially polarized core and fully paired wings, the latter occurring below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. We show that, unlike in the continuum case, the critical polarization is a nonmonotonic function of the interaction strength and vanishes in the limit of large interactions.