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arXiv:2404.11043

Exact Demonstration of pair-density-wave superconductivity in the $σ_z$-Hubbard model

Xingchuan Zhu, Junsong Sun, Shou-Shu Gong, Wen Huang, Shiping Feng, Richard T. Scalettar, Huaiming Guo

Published Apr 17, 2024• 0 citations
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Abstract

Describing and achieving `unconventional' superconductivity remains a forefront challenge in quantum many-body physics. Here we use a unitary mapping, combined with the well-established properties of the attractive Hubbard model to demonstrate rigorously a Hamiltonian with a low temperature pair-density-wave (PDW) phase. We also show that the same mapping, when applied to the widely accepted properties of the repulsive Hubbard model, leads to a Hamiltonian exhibiting triplet $d$-wave PDW superconductivity and an unusual combination of ferro- and antiferro-magnetic spin correlations. We then demonstrate the persistence of the $d$-wave PDW in a Hamiltonian derived from the mapping of the extended $t$-$J$ model in the large-$U$ limit. Furthermore, through strategic manipulation of the nearest-neighbor hopping signs of spin-down electrons, we illustrate the attainability of PDW superconductivity at other momenta. The intertwining of different magnetic and exotic pairing correlations noted here may have connections to experimental observations in spin-triplet candidates like UTe$_2$.

DOI
10.48550/arxiv.2404.11043

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Exact Demonstration of pair-density-wave superconductivity in the σzσ_zσz​-Hubbard model
Describing and achieving `unconventional' superconductivity remains a forefront challenge in quantum many-body physics. Here we use a unitary mapping, combined with the well-established properties of the attractive Hubbard model to demonstrate rigorously a Hamiltonian with a low temperature pair-density-wave (PDW) phase. We also show that the same mapping, when applied to the widely accepted properties of the repulsive Hubbard model, leads to a Hamiltonian exhibiting triplet ddd-wave PDW superconductivity and an unusual combination of ferro- and antiferro-magnetic spin correlations. We then demonstrate the persistence of the ddd-wave PDW in a Hamiltonian derived from the mapping of the extended ttt-JJJ model in the large-UUU limit. Furthermore, through strategic manipulation of the nearest-neighbor hopping signs of spin-down electrons, we illustrate the attainability of PDW superconductivity at other momenta. The intertwining of different magnetic and exotic pairing correlations noted here may have connections to experimental observations in spin-triplet candidates like UTe2_22​.
Describing and achieving ``unconventional'' superconductivity remains a forefront challenge in quantum many-body physics. Here, we use a unitary mapping, combined with the well-established properties of the attractive Hubbard model, to demonstrate rigorously a Hamiltonian with a low-temperature pair-density-wave (PDW) phase. We also show that the same mapping, when applied to the widely accepted properties of the repulsive Hubbard model, leads to a Hamiltonian exhibiting triplet ddd-wave PDW superconductivity and an unusual combination of ferro- and antiferromagnetic spin correlations. We then demonstrate the persistence of the ddd-wave PDW in a Hamiltonian derived from the mapping of the extended $t\text{\ensuremath{-}}J$ model in the large-UUU limit. Furthermore, through strategic manipulation of the nearest-neighbor hopping signs of spin-down electrons, we illustrate the attainability of PDW superconductivity at other momenta. The intertwining of different magnetic and exotic pairing correlations noted here may have connections to experimental observations in spin-triplet candidates such as UTe2{\mathrm{UTe}}_{2}UTe2​.
Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing (px,pyp_x,p_ypx​,py​) or (dxz,dyz)d_{xz}, d_{yz})dxz​,dyz​) orbitals on the square lattice. For minimal interorbital ttt-JJJ or ttt-VVV on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate dxyd_{xy}dxy​ pair density wave (ddd-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal dxyd_{xy}dxy​ pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-222 PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in ppp-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.
Pair-density wave (PDW) is a long-sought exotic state with oscillating superconducting order without external magnetic field. So far it has been rare in establishing a 2D microscopic model with PDW long-range order in its ground state. Here, we propose to study PDW superconductivity in a minimal model of spinless fermions (or spin-polarized electrons) on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interaction V_{1} and V_{2}, respectively. By performing a state-of-the-art density-matrix renormalization group study of this t-V_{1}-V_{2} model at finite doping on six-leg and eight-leg honeycomb cylinders, we show that the ground state exhibits PDW ordering (namely quasi-long-range order with a divergent PDW susceptibility). Remarkably this PDW state persists on the wider cylinder with 2D-like Fermi surfaces. To the best of our knowledge, this is probably the first controlled numerical evidence of PDW in systems with 2D-like Fermi surfaces.
Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the ttt-t′t^\primet′ Hubbard Model
The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-TcT_cTc​ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the ttt-t′t^\primet′ Hubbard model. On the electron-doped side, we find a ddd-wave superconducting (dSC) regime, supporting the scenario of high-TcT_cTc​ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near (0,π)(0, π)(0,π), distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-TcT_cTc​ superconductors.
A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with ddd-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive Vpd{V}_{pd}Vpd​ interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive Vpd{V}_{pd}Vpd​, the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.
In quantum materials, the electronic interaction and the electron-phonon coupling are in general two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, mediated by phonons, has been unveiled in one-dimensional (1D) copper-oxide chain compound. Yet it is unclear how this strong near-neighbor (NN) attraction VVV influences the superconductivity pairing. In this work, we employ the density-matrix renormalization group (DMRG) method to study this experiment-relevant extended Hubbard model with on-site Coulomb repulsion U>0U>0U>0 and NN attraction V<0V<0V<0, relevant for the 1D cuprate chain and likely other similar transition-metal materials. We find this extended ttt-UUU-VVV model hosts a rich quantum phase diagram consisting of the spin density wave phase, phase separation phases, the Tomonaga-Luttinger liquid (TLL) phase, and especially an intriguing TLL regime with divergent superconducting susceptibility and dominant spin-triplet pair correlations. Upon doping, such a spin-triplet pairing regime can be further broadened in the parameter space and extends to larger UUU. Our results show robust triplet pairing induced by attractive interaction VVV, offering a feasible mechanism to realize ppp-wave superconductivity in 1D cuprates.