Phase diagram of exciton condensate in doped two-band Hubbard model

Kuneš, J.

doi:10.1103/physrevb.90.235140

Cited by 34 publications

(38 citation statements)

References 38 publications

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“…Within the J-freezing region, even the j = 1/2 electrons show NFL behavior, and the single-band description for j = 1/2 is not valid anymore. Accordingly, the J-freezing crossover line delimits the region of validity of the single-band description.Besides the paramagnetic phase, we also investigate the excitonic magnetism (EM) near n = 4 [10, 12,13,39]. To access such a symmetry broken phase, we introduce the off-diagonal components of the Green function and define the order parameter of the exciton condensed phase as ∆ j m jm = c † jm c j m , where j = j.…”

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“…Besides the paramagnetic phase, we also investigate the excitonic magnetism (EM) near n = 4 [10, 12,13,39]. To access such a symmetry broken phase, we introduce the off-diagonal components of the Green function and define the order parameter of the exciton condensed phase as ∆ j m jm = c † jm c j m , where j = j.…”

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confidence: 99%

“…We find two types of magnetism: Antiferromagnetism (AFM) and ferromagnetism (FM) at different fillings. At n = 4 an AFM excitonic state appears at intermediate interaction strength [10,[39][40][41][42]. The corresponding region is located around the metal-insulator transition point of the paramagnetic calculations, U c /D ∼ 3.5.…”

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J Freezing and Hund’s Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models

et al. 2017

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We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with continuous-time quantum Monte Carlo. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J = L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a non-trivial flavor selectivity and energy dependence. Furthermore, in the regions near n = 2 and n = 4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n = 4 and discuss the relevance of our results for real materials.PACS numbers: 71.10. Hf, 71.15.Rf, 71.30.+h, 75.25.Dk Introduction. In 4d and 5d transition metal oxides the interplay and competition between kinetic energy, spinorbit coupling (SOC) and correlation effects results in several interesting phenomena, such as spin-orbit assisted Mott transitions [1][2][3][4][5][6], unconventional superconductivity [9, 10], topological phases [11], exciton condensation [10, 12,13], or exotic magnetic orders [14,15]. Transition metal oxides involving 4d and 5d electrons show diverse structures like the Ruddlesden-Popper series [1, 9], double perovskite, [14][15][16] two-dimensional honeycomb geometry [3][4][5][6][7][8] or pyrochlore lattices [17]. In an octahedral environment, as in most of the 4d and 5d materials mentioned above, the five d orbitals are split into low energy t 2g and higher energy e g levels. The SOC further splits the low energy t 2g levels into a so-called j = 1/2 doublet and j = 3/2 quadruplet. The energy separation between the j = 1/2 and j = 3/2 bands is proportional to the strength of the SOC. Existing ab-initio density functional theory calculations [17,18] suggest that in some materials a multiorbital description including both the j = 1/2 and j = 3/2 subbands should be considered.Most theoretical studies of 4d and 5d systems have focused on material-specific models with fixed electronic filling. Here we follow a different strategy and explore the possible states that emerge from a multiband Hubbard model with spin-orbit coupling at arbitrary filling. This allows us to investigate unexplored regions in parameter space which may exhibit interesting phenomena. Specifically, by performing a systematic analysis of the local J moment susceptibility (J = L + S) as a function of Coulomb repulsion U , Hund's coupling J H , spin-orbit coupling λ and filling n, we identify Mott-Hubbard insulating phases and complex metallic states. We find a J-freezing crossover between a Fermi liquid (FL) and a non-Fermi liquid (NFL) phase where the latter shows a distinct flavor selectivity that originates from the SOC. In addition, we observe a strong asymmetry in the metallic phase between filling n = 2 and n = 4 with properties reminiscent of the atomic Hund'...

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J Freezing and Hund’s Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models

et al. 2017

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“…We then generalize this procedure by introducing a stochastic optimization algorithm that exploits the space of single-particle bases and show that V j3/2BA is very close to optimal within the parameter space investigated. Our findings enable more efficient DMFT simulations of materials with strong spin-orbit coupling.Introduction.-Spin-orbit coupling (SOC) is an essential ingredient in the study of exotic phases in correlated electron systems [1], such as unconventional superconductivity in 4d transition-metal oxides [2-9], topological phases of matter in quantum spin-Hall insulators [10][11][12], excitonic insulators [13][14][15][16][17] or Kitaev-model-based insulators [18][19][20][21][22][23], to mention a few. A prototypical minimal model that includes the interplay between spinorbit coupling and correlations is the relativistic multiorbital Hubbard model.…”

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Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models

2020

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We present a strategy to alleviate the sign problem in continuous-time quantum Monte Carlo (CTQMC) simulations of the dynamical-mean-field-theory (DMFT) equations for the spin-orbitcoupled multi-orbital Hubbard model. We first identify the combinations of rotationally invariant Hund coupling terms present in the relativistic basis which lead to a severe sign problem. Exploiting the fact that the average sign in CTQMC depends on the choice of single-particle basis, we propose a bonding-antibonding basis (V j3/2BA ) which shows an improved average sign compared to the widely used relativistic basis for most parameter sets investigated. We then generalize this procedure by introducing a stochastic optimization algorithm that exploits the space of single-particle bases and show that V j3/2BA is very close to optimal within the parameter space investigated. Our findings enable more efficient DMFT simulations of materials with strong spin-orbit coupling.Introduction.-Spin-orbit coupling (SOC) is an essential ingredient in the study of exotic phases in correlated electron systems [1], such as unconventional superconductivity in 4d transition-metal oxides [2-9], topological phases of matter in quantum spin-Hall insulators [10][11][12], excitonic insulators [13][14][15][16][17] or Kitaev-model-based insulators [18][19][20][21][22][23], to mention a few. A prototypical minimal model that includes the interplay between spinorbit coupling and correlations is the relativistic multiorbital Hubbard model. Its non-relativistic counterpart has been intensively investigated in the past and shows a rich phase diagram [14,[24][25][26]. The relativistic multiorbital Hubbard model [4,7,[15][16][17]27], however, is much less understood since the choice of algorithms is strongly limited due to the extra computational complications associated with (multi-) spin-orbit-coupled degrees of freedom.One of the promising formalisms to investigate the Hubbard model and its generalizations is the dynamical mean-field theory (DMFT) [28,29] that has provided important insights into multi-orbital physics also in combination with ab-initio calculations for real materials [30][31][32]. The continuous-time quantum Monte Carlo method (CTQMC) [33], particularly the hybridization expansion algorithm (CTHYB) [34,35] is the most widely used impurity solver in multi-orbital DMFT calculations. However, CTHYB suffers from the notorious sign problem when the SOC is included in the calculations. The sign problem grows exponentially with inverse temperature [36,37], and typically prevents the study of lowtemperature symmetry-broken phases. Alleviating the sign problem in CTHYB would help improve our understanding of phenomena determined by the interplay of spin-orbit coupling and correlations [2,8,9,38,39].For Quantum Monte Carlo (QMC) algorithms based on auxiliary fields, there have been various successful advances which unveil the origin of the sign problem

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“…[13]. The inclusion of an interlayer or interband interaction opens the possibility of exciton formation and condensation, which has been studied using determinantal Monte Carlo simulations [14], exact diagonalization [15], DMFT [16,17], and various other theoretical approaches [18,19].…”

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Superfluidity and density order in a bilayer extended Hubbard model

et al. 2015

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We use cellular dynamical mean-field theory to study the phase diagram of the square lattice bilayer Hubbard model with an interlayer interaction. The layers are populated by two-component fermions, and the densities in both layers and the strength of the interactions are varied. We find that an attractive interlayer interaction can induce a checkerboard density-ordered phase and superfluid phases, with either interlayer or intralayer pairing. Remarkably, the latter phase does not require an intralayer interaction to be present: it can be attributed to an induced attractive interaction caused by density fluctuations in the other layer.

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Phase diagram of exciton condensate in doped two-band Hubbard model

Cited by 34 publications

References 38 publications

J Freezing and Hund’s Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models

J Freezing and Hund’s Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models

Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models

Superfluidity and density order in a bilayer extended Hubbard model

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