Phase transitions in the three-dimensional Falicov–Kimball model

Žonda, Martin; Farkašovský, Pavol; Čenčariková, Hana

doi:10.1016/j.ssc.2009.08.035

Cited by 18 publications

(28 citation statements)

References 28 publications

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“…We are utilizing a combination of a sign-problem-free Monte Carlo (MC) method [54,56,71,118,119] with a nonequilibrium Green's-function technique [120,121], which allows us to address nonequilibrium steady-state charge transport in the heterostructure [73,93]. This method takes advantage of the fact that the occupation numbers n f j = f † j f j of the localized f particles are integrals of motion and, therefore, their distribution does not change in time.…”

Section: B Methodsmentioning

confidence: 99%

“…As this is a single particle problem, the trace can be calculated efficiently using exact numerical diagonalization. The sum over configurations w can then be calculated using a Metropolis algorithm based MC method [54,56,71,118,119,123].…”

Section: Decoupled Systemmentioning

confidence: 99%

“…Note, that any disruption of the checkerboardordering, which cannot be avoided when leaving the PHS point, leads to the formation of sub-gap states or bands in the systems DOS [54,56,68,93]. However, the transmission through these sub-gap states in the vicinity of the PHS point is negligible for sufficiently broad system [93].…”

Section: Particle-hole Symmetric Casementioning

confidence: 99%

“…The simplest of these models is the Falicov-Kimball model (FKM) [48] in which the itinerant electrons interact with localized particles. The ground state of the spinless FKM at the particle-hole symmetric (PHS) point is a charge density wave (CDW) phase for any finite * martin.zonda@physik.uni-freiburg.de Coulomb interaction on a bipartite lattice in dimension two or higher [49][50][51] and this phase is stable up to finite critical temperatures [52][53][54][55][56]. However, it was also proven that a segregated phase, which is a special case of phase separation where the heavy particles (ions) and electrons reside in separate domains, is the ground state in the limit of infinite Coulomb interaction of the spinless version of the FKM [57][58][59][60][61][62].…”

Section: Introductionmentioning

confidence: 99%

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Electronic transport through correlated electron systems with nonhomogeneous charge orderings

2020

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The spinless Falicov-Kimball model exhibits outside the particle-hole symmetric point different stable nonhomogeneous charge orderings. These include the well known charge stripes and a variety of orderings with phase separated domains, which can significantly influence the charge transport through the correlated electron system. We show this by investigating a heterostructure, where the Falicov-Kimball model on a finite two-dimensional lattice is located between two non-interacting semi-infinite leads. We use a combination of nonequilibrium Green's functions techniques with a signproblem-free Monte Carlo method for finite temperatures or simulated annealing technique for the ground state to address steady-state transport through the system. We show that different groundstate phases of the central system can lead to simple metallic-like or insulating charge transport characteristics, but also to more complicated current-voltage dependencies reflecting a multi-band character of the transmission function. Interestingly, with increasing temperature, the orderings tend to form transient phases before the system reaches the disordered phase. This leads to nontrivial temperature dependencies of transmission function and charge current.

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Section: B Methodsmentioning

confidence: 99%

Section: Decoupled Systemmentioning

confidence: 99%

Section: Particle-hole Symmetric Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electronic transport through correlated electron systems with nonhomogeneous charge orderings

2020

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“…Under these conditions, the FK model undergoes, at low temperatures, a transition to the charge density wave (CDW) ordered state, with Q = (π, π) ordering wave-vector. The transition is continuous for large U with some evidence pointing to a change to discontinous transitions for small U [39,40]. The application of our algorithm yields all-temperature results unlike standard Metropolis sampling over the immobile fermions.…”

Section: Introduction -mentioning

confidence: 99%

Minimal energy ensemble Monte Carlo algorithm for the partition function of fermions coupled to classical fields

et al. 2016

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Models of non-interacting fermions coupled to auxilliary classical degrees of freedom are relevant to the understanding of a wide variety of problems in many body physics, e.g. the description of manganites, diluted magnetic semiconductors or strongly interacting electrons on lattices. Monte Carlo sampling over the classical fields is a powerful, yet notoriously challenging, method for this class of problems -it requires the solution of the fermion problem for each classical field configuration. Conventional Monte Carlo methods minimally utilize the information content of these solutions by extracting single temperature properties. We present a flat-histogram Monte Carlo algorithm that simulates a novel statistical ensemble which allows to acquire the full thermodynamic information, i.e. the partition function at all temperatures, of sampled classical configurations. Introduction -Bilinear Hamiltonians of lattice fermions coupled to classical degrees of freedom (continuous or discrete) are ubiquituous in contemporary manybody physics. These often arise as suitable approximations in the description of systems where many different degrees of freedom contrive to yield complex and interesting physics. In these cases, some subsystem is treated classically as e.g. localized spins in double-exchange models [1][2][3], models of Mn-doped (III, IV) semiconductors [4], the Ising t-J model [5], adiabatic phonons in polaron models [6][7][8][9], or one species of fermions in the Falicov-Kimball model [9][10][11]. Exactly solvable models can also take this form, such as the seminal honeycomb lattice Kitaev model [12] where interacting spins are mapped onto Majorana fermions coupled to static gauge fields. More generally, auxiliary field methods, e.g. based on the Hubbard-Stratonovich transformation, allow to decouple fermion-fermion or fermion-boson interactions -the fields are then treated classically in conjunction with the application of the Suzuki-Trotter decomposition [13,14] (see [15] for a recent approximate scheme with static fields).

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Phase transitions in the Falicov–Kimball model away from half-filling

Žonda

2012

Phase Transitions

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Phase transitions in the three-dimensional Falicov–Kimball model

Cited by 18 publications

References 28 publications

Electronic transport through correlated electron systems with nonhomogeneous charge orderings

Electronic transport through correlated electron systems with nonhomogeneous charge orderings

Minimal energy ensemble Monte Carlo algorithm for the partition function of fermions coupled to classical fields

Phase transitions in the Falicov–Kimball model away from half-filling

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