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arXiv:1007.5251 · Physical Review B

Exotic paired phases in ladders with spin-dependent hopping

Adrian E. Feiguin, Matthew P. A. Fisher

Published Mar 4, 2011• 16 citations
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Abstract

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.

DOI
10.1103/physrevb.83.115104

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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 ddd-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.
We propose a model for realizing exotic paired states in cold Fermi gases by using a spin-dependent optical lattice to engineer mismatched Fermi surfaces for each hyperfine species. The BCS phase diagram shows a stable paired superfluid state with coexisting pockets of momentum space with gapless unpaired carriers, similar to the Sarma state in polarized mixtures, but in our case the system is unpolarized. We propose the possible existence of an exotic "Cooper-pair Bose-metal" phase, which has a gap for single fermion excitations but gapless and uncondensed "Cooper-pair" excitations residing on a "Bose surface" in momentum space.
The study of non-Fermi liquids sheds light on unconventional phenomena in condensed matter systems that lie beyond the scope of Landau Fermi liquid theory. One intriguing example is the Bose metal, characterized by an uncondensed bosonic ground state. However, constructing a Bose metal phase in two dimensions (2D) remains a significant challenge. Utilizing constraint path quantum Monte Carlo and functional renormalization group methods on a fermionic system with spin anisotropy in a 2D lattice, we reveal the emergence of a Cooper pair Bose metal (CPBM) phase in a highly anisotropic regime ($\ensuremath{\alpha}<0.30$) 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 dxy{d}_{xy}dxy​ 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.
We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the ddd-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B 75, 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the NNN-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power-law transverse density-density correlations. While we have already presented results on this latter phase elsewhere [M. S. Block et al., Phys. Rev. Lett. 106, 046402 (2011)], we will expand upon those results in this work. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.
Developing a theoretical framework to access the quantum phases of itinerant bosons or fermions in two dimensions that exhibit singular structure along surfaces in momentum space but have no quasiparticle description remains a central challenge in the field of strongly correlated physics. In this paper we propose that distinctive signatures of such two-dimensional (2D) strongly correlated phases will be manifest in quasi-one-dimensional ``NNN-leg ladder'' systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the NNN-leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional ddd-wave-correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density-matrix renormalization-group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory provide compelling evidence for the existence of an unusual strong-coupling phase of bosons on the two-leg ladder, which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders, which could likewise reveal fingerprints of such 2D non-Fermi-liquid phases.
The study of non-Fermi liquids sheds light on unconventional phenomena in condensed matter systems that lie beyond the scope of Landau Fermi liquid theory. One intriguing example is the Bose metal, characterized by an uncondensed bosonic ground state. However, constructing a Bose metal phase in two dimensions (2D) remains a significant challenge.} Utilizing constraint path quantum Monte Carlo and functional renormalization group methods on a fermionic system with spin anisotropy in a 2D lattice, we reveal the emergence of a Cooper pair Bose metal (CPBM) phase in a highly anisotropic regime (α<0.30α< 0.30α<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 dxyd_{xy}dxy​ 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.
The Cooper pair Bose metal (CPBM) is a non-superfluid 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', carrier filling n, and spin anisotropy alpha, using large-scale constrained-path quantum Monte Carlo simulations. A moderate NNN hopping (t'/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' = 0. Interestingly, t' 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' and carrier filling n. For small t', d_xy-wave correlations dominate across the entire filling range. In contrast, for larger t', 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 non-superfluid bosonic matter in cold-atom and correlated-electron systems.