Possible phase separation in square and honeycomb Hubbard model: A variational cluster study

Fang, Kun; Fernando, Gayanath; Balatsky, Alexander V.; Kocharian, Armen

doi:10.1016/j.physleta.2015.06.059

Cited by 4 publications

(2 citation statements)

References 48 publications

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“…[3]). What is known has been deduced from numerical simulations, such as via Random Phase Approximation [4], mean field theories [5], cluster theories [6], or functional renormalization group techniques [7,8]. Recent calculations on modest system sizes have utilized Quantum Monte Carlo (QMC) techniques [4,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

Krieg

Luu

Ostmeyer

et al. 2019

Computer Physics Communications

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We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix inversions and the second order Omelyan integrator with Hasenbusch acceleration on different time scales for molecular dynamics. We demonstrate how an arbitrary number of Hasenbusch mass terms can be included into this geometry and find that the optimal speed depends weakly on the choice of the number of Hasenbusch masses and their values. As such, the tuning of these masses is amenable to automization and we present an algorithm for this tuning that is based on the knowledge of the dependence of solver time and forces on the Hasenbusch masses. We benchmark our algorithms to systems where direct numerical diagonalization is feasible and find excellent agreement. We also simulate systems with hexagonal lattice dimensions up to 102 × 102 and N t = 64. We find that the Hasenbusch algorithm leads to a speed up of more than an order of magnitude.

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Section: Introductionmentioning

confidence: 99%

Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

Krieg

Luu

Ostmeyer

et al. 2019

Computer Physics Communications

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show abstract

“…Halboth and Metzner [35] studied a two-dimensional Hubbard model using functional renormalization group (RG) method, and revealed Pomeranchuk instability and nematic order. More recently, the square lattice Hubbard model is studied by variational cluster approximation [45,46] and found to display a local nematic phase under certain circumstances, which might be applied to understand the intra-unit-cell electronic nematicity observed in the scanning tunneling spectroscopy (STS) measurements by Lawler et al [13].…”

Section: Introductionmentioning

confidence: 99%

Unconventional non-Fermi liquid state caused by nematic criticality in cuprates

2016

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2-wave superconducting dome of cuprates, the massless nodal fermions interact strongly with the quantum critical fluctuation of nematic order. We study this problem by means of the renormalization group approach and show that, the fermion damping rate w S Im R | ( )|vanishes more rapidly than the energy ω and the quasiparticle residue  Z 0 f in the limit w  0. The nodal fermions thus constitute an unconventional non-Fermi liquid that represents an even weaker violation of Fermi liquid theory than a marginal Fermi liquid. We also investigate the interplay of quantum nematic critical fluctuation and gauge-potential-like disorder, and find that the effective disorder strength flows to the strong coupling regime at low energies. Therefore, even an arbitrarily weak disorder can drive the system to become a disorder controlled diffusive state. Based on these theoretical results, we are able to understand a number of interesting experimental facts observed in curpate superconductors.

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Spin-orbit coupling, electron transport and pairing instabilities in two-dimensional square structures

et al. 2016

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Rashba spin-orbit effects and electron correlations in the two-dimensional cylindrical lattices of square geometries are assessed using mesoscopic two-, three- and four-leg ladder structures. Here the electron transport properties are systematically calculated by including the spin-orbit coupling in tight binding and Hubbard models threaded by a magnetic flux. These results highlight important aspects of possible symmetry breaking mechanisms in square ladder geometries driven by the combined effect of a magnetic gauge field spin-orbit interaction and temperature. The observed persistent current, spin and charge polarizations in the presence of spin-orbit coupling are driven by separation of electron and hole charges and opposite spins in real-space. The modeled spin-flip processes on the pairing mechanism induced by the spin-orbit coupling in assembled nanostructures (as arrays of clusters) engineered in various two-dimensional multi-leg structures provide an ideal playground for understanding spatial charge and spin density inhomogeneities leading to electron pairing and spontaneous phase separation instabilities in unconventional superconductors. Such studies also fall under the scope of current challenging problems in superconductivity and magnetism, topological insulators and spin dependent transport associated with numerous interfaces and heterostructures.

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Possible phase separation in square and honeycomb Hubbard model: A variational cluster study

Cited by 4 publications

References 48 publications

Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

Unconventional non-Fermi liquid state caused by nematic criticality in cuprates

Spin-orbit coupling, electron transport and pairing instabilities in two-dimensional square structures

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