arXiv subjects

R. Torsten Clay

Publications and source records attributed to R. Torsten Clay.

11 recordsLinked to original sources

arXiv2026

Benchmarking the accuracy of superconducting pair-pair correlations within Constrained Path Quantum Monte Carlo

Ground state properties of the Hubbard model are of fundamental importance to understand the mechanism of unconventional superconductivity in the high-T_c cuprates and other materials. One of the most powerful numerical methods for strongly interacting models is quantum Monte Carlo, which however faces a fundamental limitation, the Fermion sign problem. The sign problem can be mitigated using approximate methods such as Constrained Path Monte Carlo, but additional approximations must be made in order to measure different observables, particularly for operators that do not commute with the Hamiltonian. We examine critically the most commonly used approximation, back propagation, as well as a recently proposed constraint release measurement technique. In comparisons with a variety of systems that can be solved numerically exactly by other methods, we find that back propagation tends to underestimate superconducting pair-pair correlations. The constraint release technique can provide accurate results, with the disadvantages that it much more computationally expensive and reintroduces the sign problem.

cond-mat.str-el↗

arXiv2025

Comment on "Superconductivity and Mott Physics in Organic Charge Transfer Materials"

Menke et al. recently claimed that superconductivity (SC) in the $\kappa$-phase organic charge-transfer solids (CTS) can be understood within the two-dimensional half-filled anisotropic triangular-lattice Hubbard model. Experimentally, $\kappa$-CTS are mostly but not always antiferromagnetic (AFM) at ambient pressure and SC appears under pressure. In apparent agreement with this observation, Menke et al. found AFM ground states for small $t/U$ and SC over a small region at the interface of AFM and Fermi liquid ground states with increasing $t/U$ at fixed $t'/t$, where $U$ is the Hubbard repulsion. Menke et al's computational results directly contradict those obtained using exact diagonalization and Path Integral Renormalization Group approaches. It is clearly of interest to determine the origin of this discrepancy, especially in view of the facts that (a) related arguments continue to persist in the context of cuprate SC superconductivity (which however involves doping), and (b) there exist CTS in which SC is not proximate to AFM, but is separated by an intermediate charge-disproportionated phase. Here we show that Menke et al's conclusion regarding SC is incorrect and originates from a flawed assumption.

cond-mat.supr-con↗

arXiv2024

Computational Demonstrations of Density Wave of Cooper Pairs and Paired-Electron Liquid in the Quarter-Filled Band -- a Brief Review

There has been strong interest recently in the so-called Cooper pair density wave, subsequent to the proposition that such a state occurs in the hole-doped cuprate superconductors. As of now there is no convincing demonstration of such a state in the cuprate theoretical literature. We present here a brief but complete review of our theoretical and computational work on the paired-electron crystal (PEC), which has been also experimentally seen in the insulating phase proximate to superconductivity (SC) in organic charge-transfer solid (CTS) superconductors. Within our theory, SC in the CTS does indeed evolve from the PEC. A crucial requirement for the finding of the PEC is that the proper carrier density of one charge carrier per two sites is taken into consideration at the outset. Following the discussion of CTS superconductors, we briefly discuss how the theory can be extended to understand the phase diagram of the cuprate superconductors that has remained mysterious after nearly four decades of the discovery of SC in this family.

cond-mat.str-el↗

arXiv2023

Valence Transition Theory of the Pressure-Induced Dimensionality Crossover in Superconducting Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$

More than three decades after the discovery of superconductivity (SC) in the cuprates, the nature of the "normal" state and the mechanism of SC remain mysterious. One popular theoretical approach has been to treat the CuO$_2$ layer as coupled two-leg one-band Hubbard ladders. In the undoped two-leg ladder spin-singlets occupy ladder rungs, and doped ladders are characterized by superconducting correlations with quasi-long range order (quasi-LRO). Pressure-induced SC in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ (SCCO) has long been explained within one-band ladder theories. The dramatic pressure-driven crossover from quasi one-to-two dimensional (1D-to-2D) transport and the simultaneous vanishing of the spin gap due to ladder singlets in the metallic state preceding SC however lie outside the scope of ladder-based theories. Recent demonstration of rapid decay of superconducting correlations with distance within a realistic multiband model of the cuprate ladder gives additional credence to this viewpoint. Here we show that the assumption of pressure-driven increase in hole concentration in the ladders cannot explain the dimensionality crossover. The dimensionality crossover is due to discrete change in Cu-ion ionicity accompanied by transfer of holes from the Cu to O-ions, leading to "negative charge-transfer gap". Our theory of valence transition driven dimensionality crossover in SCCO provides a generic explanation of the very large increase in charge carrier density at critical doping concentrations in both hole and electron doped layered cuprates We propose a falsifiable experimental test of our theory.

cond-mat.str-el↗

arXiv2023

Doping asymmetry in the three-band Hamiltonian for cuprate ladders: failure of the standard model of superconductivity in cuprates

The relevance of the single-band two-dimensional Hubbard model to superconductivity in the doped cuprates has recently been questioned, based on Density matrix Renormalization Group (DMRG) computations on extended t-J models that found superconductivity over unrealistically broad doping region upon electron-doping, yet complete absence of superconductivity for hole-doping. We report very similar results from DMRG calculations on Cu$_2$O$_3$ two-leg ladder within the parent three-band correlated-electron Hamiltonian. The strong asymmetry found in our calculations are in contradiction to the deep and profound symmetry between electron- and hole-doped cuprate superconductors, apart from their critical temperatures, that has been found from recent experiments.

cond-mat.str-el↗

arXiv2023

Density Matrix Renormalization Group study of superconducting pairing near the quarter-filled Wigner crystal

Charge ordering is often found in the phase diagram of unconventional superconductors in close proximity to the superconducting state. This has led to the suggestion that fluctuations of charge order can mediate superconducting pairing. While several mechanisms can lead to charge order, one common mechanism is the long-range Coulomb interaction, resulting in a Wigner crystal charge ordered state. For an electron density of 0.5 per site we investigate the extended Hubbard model on the two-dimensional square lattice using exact diagonalization and density matrix renormalization group methods. Our results show that the strength of pairing decreases with the nearest-neighbor Coulomb interaction strength $V$ and remains weaker than the tendency of pairing for non-interacting electrons.

cond-mat.str-el↗

arXiv2021

Absence of Luther-Emery Superconducting Phase in the Three-Band Model for Cuprate Ladders

Correlated-electron theories of superconductivity in layered cuprates often start from the premise of a gapped spin-liquid phase proximate to the superconducting state. This assumption is justified based on analytical and numerical demonstrations of a superconducting Luther-Emery phase in the doped 2-leg one-band Hubbard ladder, and the perceived analogy between coupled ladders and the two dimensional CuO2 layer. We demonstrate from accurate density matrix renormalization group studies the absence of the superconducting Luther-Emery phase in the doped 2-leg three-band ladder consisting of both copper and oxygen, even as the spin gap is large in the undoped three-band ladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen atoms, density-density rather than pairing correlations are dominant at long range. This result is equally valid whether or not the oxygens outside the ladder proper, over and above the rung and leg oxygens, are included in the computation. These results demonstrate the critical importance of oxygen orbitals, and raise disturbing questions about the applicability of many of the existing correlated-electron theories of superconductivity.

cond-mat.str-el↗

arXiv2015

Coulomb Enhanced Superconducting Pair Correlations in the Frustrated Quarter-Filled Band

A necessary condition for superconductivity (SC) driven by electron correlations is that electron-electron (e-e) interactions enhance superconducting pair-pair correlations, relative to the noninteracting limit. We report high-precision numerical calculations of the ground state within the frustrated two-dimensional (2D) Hubbard Hamiltonian for a wide range of carrier concentration $ρ$ (0 < $ρ$ <1) per site. We find that long range superconducting pair correlations are enhanced only for $ρ$ $\simeq$ 0.5. At all other fillings e-e interactions mostly suppress pair correlations. The enhancement of pair correlations is driven by the strong tendency to local singlet bond formation and spin gap (SG) in $ρ$ = 0.5, in lattices with quantum fluctuation. We also report determinantal quantum Monte Carlo (DQMC) calculations that are in strong agreement with our ground state results. Our work provides a key ingredient to the mechanism of SC in the 2D organic charge-transfer solids (CTS), and many other unconventional superconductors with frustrated crystal lattices and $ρ$ $\simeq$ 0.5, while explaining the absence of SC in structurally related materials with substantially different $ρ$.

cond-mat.supr-con↗

arXiv2011

Is there a common theme behind the correlated-electron superconductivity in organic charge-transfer solids, cobaltates, spinels and fullerides?

We posit that there exist deep and fundamental relationships between the above seemingly very different materials. The carrier concentration-dependences of the electronic behavior in the conducting organic charge-transfer solids and layered cobaltates are very similar. These dependences can be explained within a single theoretical model, - the extended Hubbard Hamiltonian with significant nearest neighbor Coulomb repulsion. Interestingly, superconductivity in the cobaltates seems to be restricted to bandfilling exactly or close to one-quarter, as in the organics. We show that dynamic Jahn-Teller effects and the resultant orbital ordering can lead to 1/4-filled band descriptions for both superconducting spinels and fullerides, which show evidence for both strong electron-electron and electron-phonon interactions. The orbital orderings in antiferromagnetic lattice-expanded bcc M$_3$C$_{60}$ and the superconductor are different in our model. Strong correlations, quarter-filled band and lattice frustration are the common characteristics shared by these unusual superconductors.

cond-mat.str-el↗

arXiv2011

Similarities in electronic properties of organic charge-transfer solids and layered cobaltates

The apparently counterintuitive carrier concentration-dependent electronic properties of layered cobaltates have attracted wide interest. Here we point out that very similar carrier-concentration dependence has previously been noted in strongly correlated quasi-one dimensional (quasi-1D) organic charge-transfer solids. The normal states of both families can be understood, over the entire range of carrier concentration of interest, within the extended Hubbard Hamiltonian with significant intersite Coulomb interaction. As with the charge-transfer solids, superconductivity in the cobaltates appears to be limited to bandfilling of one-quarter. We point out further that there exist other families of correlated superconductors, such as spinels, where too strong correlations, geometric lattice frustration and bandfilling of one-quarter seem to be the essential features of the unconventional superconductors.

cond-mat.str-el↗

arXiv1998

Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

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