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Physical review. B./Physical review. B

Rigorous 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 Jan 27, 2025• 1 citation
Publisher

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 antiferromagnetic spin correlations. We then demonstrate the persistence of the $d$-wave PDW in a Hamiltonian derived from the mapping of the extended $t\text{\ensuremath{-}}J$ 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 such as ${\mathrm{UTe}}_{2}$.

DOI
10.1103/physrevb.111.045158

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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\ensuremath-Jt\text{\ensuremath{-}}Jt\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​.
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​.
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The quest to understand the nature of superconductivity in the cuprates has spotlighted the pair density wave (PDW)–a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge, and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive tpp case. When the system incorporates moderate near-neighbor interactions, particularly an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When the attractive Vpp increases further, the system gives way to an unconventional d-wave superconductivity.
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.