) with wide range of filling, as proposed in [A. E. Feiguin et al., Phys. Rev. Lett. 103, 025303 (2009)]. Our findings exhibit a visible nonzero momentum Bose surface in the Cooper-pair distribution function, accompanied by a distinct signal of

{d}_{xy}

correlation between pairs. Our results highlight that spin-dependent anisotropy in the Fermi surface leads to versatile pairing forms. Platforms such as ultracold atoms in optical lattices and recently proposed altermagnets hold promise for realizing this intriguing phase.

DOI: 10.1103/physrevb.110.224522

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The Cooper pair Bose metal (CPBM) is a nonsuperfluid quantum phase in which uncondensed fermion pairs form a ``Bose surface'' in momentum space. We investigate the CPBM in the two-dimensional spin-anisotropic attractive Hubbard model by tuning the next-nearest-neighbor (NNN) hopping ${t}^{\ensuremath{'}}$, carrier filling $n$ , and spin anisotropy $\ensuremath{\alpha}$, using large-scale constrained-path quantum Monte Carlo simulations. A moderate NNN hopping ${t}^{\ensuremath{'}}/t=0.2$ substantially enlarges the CPBM region: the phase extends into weaker anisotropy regimes and coexists with a commensurate charge-density wave (CDW) near half-filling $(n>0.95)$ , where CDW order would otherwise dominate at ${t}^{\ensuremath{'}}=0$. Interestingly, ${t}^{\ensuremath{'}}$ suppresses the overall CDW peak amplitude and introduces a geometric correlation between the orientations of the Fermi and Bose surfaces: for weak Fermi-surface rotations, the Bose surface remains aligned with the lattice axes, while larger distortions drive both surfaces to rotate in tandem. Momentum-resolved pairing distributions reveal that the bosonic pairing channels are jointly controlled by ${t}^{\ensuremath{'}}$ and carrier filling $n$ . For small ${t}^{\ensuremath{'}}$, ${d}_{xy}$ -wave correlations dominate across the entire filling range. In contrast, for larger ${t}^{\ensuremath{'}}$, the dominant pairing symmetry varies with $n$ , reflecting a nontrivial interplay between frustration and density. These findings establish carrier filling and NNN hopping as complementary levers for manipulating CPBM stability and provide concrete criteria for identifying nonsuperfluid bosonic matter in cold-atom and correlated-electron systems.The Cooper pair Bose metal (CPBM) is a nonsuperfluid quantum phase in which uncondensed fermion pairs form a ``Bose surface'' in momentum space. We investigate the CPBM in the two-dimensional spin-anisotropic attractive Hubbard model by tuning the next-nearest-neighbor (NNN) hopping ${t}^{\ensuremath{'}}$, carrier filling $n$, and spin anisotropy $\ensuremath{\alpha}$, using large-scale constrained-path quantum Monte Carlo simulations. A moderate NNN hopping ${t}^{\ensuremath{'}}/t=0.2$ substantially enlarges the CPBM region: the phase extends into weaker anisotropy regimes and coexists with a commensurate charge-density wave (CDW) near half-filling $(n>0.95)$, where CDW order would otherwise dominate at ${t}^{\ensuremath{'}}=0$. Interestingly, ${t}^{\ensuremath{'}}$ suppresses the overall CDW peak amplitude and introduces a geometric correlation between the orientations of the Fermi and Bose surfaces: for weak Fermi-surface rotations, the Bose surface remains aligned with the lattice axes, while larger distortions drive both surfaces to rotate in tandem. Momentum-resolved pairing distributions reveal that the bosonic pairing channels are jointly controlled by ${t}^{\ensuremath{'}}$ and carrier filling $n$. For small ${t}^{\ensuremath{'}}$, ${d}_{xy}$-wave correlations dominate across the entire filling range. In contrast, for larger ${t}^{\ensuremath{'}}$, the dominant pairing symmetry varies with $n$, reflecting a nontrivial interplay between frustration and density. These findings establish carrier filling and NNN hopping as complementary levers for manipulating CPBM stability and provide concrete criteria for identifying nonsuperfluid bosonic matter in cold-atom and correlated-electron systems.

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Exotic paired phases in ladders with spin-dependent hopping

Adrian E. Feiguin, Matthew P. A. Fisher

Fermions in two dimensions, when subject to anisotropic spin-dependent hopping, can potentially give rise to unusual paired states in unpolarized mixtures that can behave as non-Fermi liquids. One possibility is a fully paired state with a gap for fermion excitations in which the Cooper pairs remain uncondensed. Such a ``Cooper-pair Bose-metal'' phase would be expected to have a singular Bose surface in momentum space. As demonstrated in the context of two-dimensional bosons hopping with a frustrating ring-exchange interaction, an analogous Bose-metal phase has a set of quasi-one-dimensional descendant states when put on a ladder geometry. Here we present a density matrix renormalization group study of the attractive Hubbard model with spin-dependent hopping on a two-leg ladder geometry. In our setup, one spin species moves preferentially along the leg direction, while the other does so along the rung direction. We find compelling evidence for the existence of a novel Cooper-pair Bose-metal phase in a region of the phase diagram at intermediate coupling. We further explore the phase diagram of this model as a function of hopping anisotropy, density, and interaction strength, finding a conventional superfluid phase as well as a phase of paired Cooper pairs with $d$ -wave symmetry, similar to the one found in models of hard-core bosons with ring exchange. We argue that simulating this model with cold Fermi gases on spin-dependent optical lattices is a promising direction for realizing exotic quantum states.Fermions in two dimensions, when subject to anisotropic spin-dependent hopping, can potentially give rise to unusual paired states in unpolarized mixtures that can behave as non-Fermi liquids. One possibility is a fully paired state with a gap for fermion excitations in which the Cooper pairs remain uncondensed. Such a ``Cooper-pair Bose-metal'' phase would be expected to have a singular Bose surface in momentum space. As demonstrated in the context of two-dimensional bosons hopping with a frustrating ring-exchange interaction, an analogous Bose-metal phase has a set of quasi-one-dimensional descendant states when put on a ladder geometry. Here we present a density matrix renormalization group study of the attractive Hubbard model with spin-dependent hopping on a two-leg ladder geometry. In our setup, one spin species moves preferentially along the leg direction, while the other does so along the rung direction. We find compelling evidence for the existence of a novel Cooper-pair Bose-metal phase in a region of the phase diagram at intermediate coupling. We further explore the phase diagram of this model as a function of hopping anisotropy, density, and interaction strength, finding a conventional superfluid phase as well as a phase of paired Cooper pairs with $d$-wave symmetry, similar to the one found in models of hard-core bosons with ring exchange. We argue that simulating this model with cold Fermi gases on spin-dependent optical lattices is a promising direction for realizing exotic quantum states.

arXiv:1007.5251Physical Review BMar 4, 201116 citations

\ensuremath{\alpha}<0.30

{d}_{xy}

α< 0.30

) with wide range of filling, as proposed in [A. E. Feiguin and M. P. A. Fisher, Phys. Rev. Lett. 103, 025303 (2009)]. Our findings exhibit a visible nonzero momentum Bose surface in the Cooper-pair distribution function, accompanied by a distinct signal of

d_{xy}

n

, and spin anisotropy $\ensuremath{\alpha}$, using large-scale constrained-path quantum Monte Carlo simulations. A moderate NNN hopping ${t}^{\ensuremath{'}}/t=0.2$ substantially enlarges the CPBM region: the phase extends into weaker anisotropy regimes and coexists with a commensurate charge-density wave (CDW) near half-filling

(n>0.95)

, where CDW order would otherwise dominate at ${t}^{\ensuremath{'}}=0$. Interestingly, ${t}^{\ensuremath{'}}$ suppresses the overall CDW peak amplitude and introduces a geometric correlation between the orientations of the Fermi and Bose surfaces: for weak Fermi-surface rotations, the Bose surface remains aligned with the lattice axes, while larger distortions drive both surfaces to rotate in tandem. Momentum-resolved pairing distributions reveal that the bosonic pairing channels are jointly controlled by ${t}^{\ensuremath{'}}$ and carrier filling

n

. For small ${t}^{\ensuremath{'}}$,

{d}_{xy}

-wave correlations dominate across the entire filling range. In contrast, for larger ${t}^{\ensuremath{'}}$, the dominant pairing symmetry varies with

n

, reflecting a nontrivial interplay between frustration and density. These findings establish carrier filling and NNN hopping as complementary levers for manipulating CPBM stability and provide concrete criteria for identifying nonsuperfluid bosonic matter in cold-atom and correlated-electron systems.

d

-wave symmetry, similar to the one found in models of hard-core bosons with ring exchange. We argue that simulating this model with cold Fermi gases on spin-dependent optical lattices is a promising direction for realizing exotic quantum states.