Strong Coupling Limit of the Holstein-Hubbard Model

Abstract

A pair-density-wave (PDW) is a novel superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization group (DMRG) study of an effective t-J-V model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the K and K points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge c ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.2t 2 1 J−V and t 2 1 J−V < τ + 3t2, are also checked to be satisfied.[27] The factor of 2 enhancement of 2kF could be accounted for in a fully spin-polarized ferromagnet, but we have verified that the ground-state has spin 0.

Robustness of Antiferromagnetism in the Su-Schrieffer-Heeger-Hubbard model

“…In many quantum materials, both EPC and strong electronic interactions are present; under certain circumstances they can cooperatively affect physical properties of such systems. Indeed, in the past many years, increasing experimental and theoretical progresses suggest that EPC can play an important role even in quantum systems with strong electronic correlation, for instance, in cuprates , iron-based superconductors [32][33][34][35][36][37][38][39][40][41][42][43], and in various model systems [44][45][46][47][48]. Various previous works mainly focused on the competition between AFM order induced by Coulomb interactions and other types of orders such as EPC-induced CDW .…”

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas

“…Moreover, there is plethora of recent experimental and theoretical studies of quasi-two-dimensional systems, e.g., Na CoO [ 42 ], NbSe [ 43 , 44 , 45 , 46 , 47 ], TiSe [ 48 ], TaSe [ 49 ], VSe [ 50 ], TaS [ 51 ], and other transition metals dichalcogenides [ 52 ] as well as organic conductors [ 53 , 54 ], where various charge-ordered patterns have been observed on the triangular lattice. However, for such phenomena the atomic limit of the model studies is less reliable and more realistic description includes also electron hoping term as in the extended Hubbard model [ 15 , 16 , 17 , 18 , 19 ] or coupling with phonons as in the Holstein-Hubbard model [ 55 ]. In such cases, results obtained for atomic limit can be treated as a benchmark for models including the itinerant properties of fermionic particles.…”

Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice

“…In the presence of an additional on-site electron-electron repulsion U , the system can exhibit dominant AF or CDW correlations depending on the relative magnitude of U and λ [13,14]. Interestingly, there are indications of an intermediate metallic phase between the AF and CDW phases [15][16][17][18], as well as other exotic regimes [19].…”