arXiv:cond-mat/0611583 · Physical Review Letters

Quantum Lifshitz Point in the Infinite-Dimensional Hubbard Model

F. Günther, G. Seibold, J. Lorenzana

Published Apr 25, 2007• 7 citations

Abstract

We show that the Gutzwiller variational wave function is very accurate for the computation of magnetic phase boundaries in the infinite-dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both the half-hypercubic and the hypercubic lattice, a large part of the phase diagram is occupied by an incommensurate phase, intermediate between the ferromagnetic and the paramagnetic phase. In case of the hypercubic lattice, the three phases join at a new quantum Lifshitz point at which the order parameter is critical and the stiffness vanishes.

DOI: 10.1103/physrevlett.98.176404

Related papers

Hubbard model on the infinite-dimensional diamond lattice

Giuseppe E. Santoro, Marco Airoldi, Sandro Sorella +1 more

Physical review. B, Condensed matterJun 15, 199317 citations

Route to supersolidity for the extended Bose-Hubbard model

M. Iskin

arXiv:1101.6067Physical Review AMay 31, 201172 citations

Quantum information analysis of the phase diagram of the half-filled extended Hubbard model

Cornelius Mund, Örs Legeza, R. M. Noack

arXiv:0904.4673Physical Review BJun 25, 200937 citations

Gutzwiller magnetic phase diagram of the undoped t−t′−U Hubbard model

R.S. Markiewicz, J. Lorenzana, G. Seibold

arXiv:1207.5538Physical Review BJan 13, 201017 citations

Ground-state phase diagram of the repulsive SU(3) Hubbard model in the Gutzwiller approximation

Ákos Rapp, Achim Rosch

arXiv:1102.3053Physical Review AMay 3, 201120 citations

Phase Separation in the Extended Hubbard Model at Weak Coupling

P. G. J. van Dongen

Physical Review LettersJan 2, 199542 citations

arXiv:cond-mat/0611583 · Physical Review Letters

Quantum Lifshitz Point in the Infinite-Dimensional Hubbard Model

F. Günther, G. Seibold, J. Lorenzana

Published Apr 25, 2007• 7 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.98.176404

Related papers

Hubbard model on the infinite-dimensional diamond lattice

Giuseppe E. Santoro, Marco Airoldi, Sandro Sorella +1 more

We present and study the infinite-dimensional limit of the Hubbard model on a class of non-nested bipartite lattices which generalize the two-dimensional honeycomb and three-dimensional diamond lattice, and are characterized by a semimetallic noninteracting density of states. The infinite-dimensional limit is studied by the well-known mapping onto a self-consistent one-impurity problem. This is solved using quantum Monte Carlo and second-order perturbation theory. The (U,T) phase diagram at half-filling shows a nonmagnetic semimetallic region and an antiferromagnetic insulating phase with a critical value of U for the transition at T=0 which is strictly positive, ${\mathit{U}}_{\mathit{c}}$ /t\ensuremath{\approxeq}2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at ${\mathit{U}}_{\mathit{c}}$ =0.We present and study the infinite-dimensional limit of the Hubbard model on a class of non-nested bipartite lattices which generalize the two-dimensional honeycomb and three-dimensional diamond lattice, and are characterized by a semimetallic noninteracting density of states. The infinite-dimensional limit is studied by the well-known mapping onto a self-consistent one-impurity problem. This is solved using quantum Monte Carlo and second-order perturbation theory. The (U,T) phase diagram at half-filling shows a nonmagnetic semimetallic region and an antiferromagnetic insulating phase with a critical value of U for the transition at T=0 which is strictly positive, ${\mathit{U}}_{\mathit{c}}$/t\ensuremath{\approxeq}2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at ${\mathit{U}}_{\mathit{c}}$=0.

Physical review. B, Condensed matterJun 15, 199317 citations

Route to supersolidity for the extended Bose-Hubbard model

M. Iskin

We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site ( $U$ ) and nearest-neighbor ( $V$ ) repulsions. For $d$ -dimensional hypercubic lattices, when $2\mathit{dV}<U$ , it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when $2\mathit{dV}>U$ , in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site ($U$) and nearest-neighbor ($V$) repulsions. For $d$-dimensional hypercubic lattices, when $2\mathit{dV}<U$, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when $2\mathit{dV}>U$, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.

arXiv:1101.6067Physical Review AMay 31, 201172 citations

Quantum information analysis of the phase diagram of the half-filled extended Hubbard model

Cornelius Mund, Örs Legeza, R. M. Noack

We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.

arXiv:0904.4673Physical Review BJun 25, 200937 citations

Gutzwiller magnetic phase diagram of the undoped t−t′−U Hubbard model

R.S. Markiewicz, J. Lorenzana, G. Seibold

We calculate the magnetic phase diagram of the half-filled $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model as a function of ${t}^{\ensuremath{'}}$ and $U$ , within the Gutzwiller approximation plus random-phase approximation. As $U$ increases, the system first crosses over to one of a wide variety of incommensurate phases, whose origin is clarified in terms of double nesting. We evaluate the stability regime of the incommensurate phases by allowing for symmetry breaking with regard to the formation of spin spirals, and find a crossover to commensurate phases as $U$ increases and a full gap opens. The results are compared with a variety of other recent calculations, and in general good agreement is found. For parameters appropriate to the cuprates, double occupancy should be only mildly suppressed in the absence of magnetic order, inconsistent with a strong-coupling scenario.We calculate the magnetic phase diagram of the half-filled $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model as a function of ${t}^{\ensuremath{'}}$ and $U$, within the Gutzwiller approximation plus random-phase approximation. As $U$ increases, the system first crosses over to one of a wide variety of incommensurate phases, whose origin is clarified in terms of double nesting. We evaluate the stability regime of the incommensurate phases by allowing for symmetry breaking with regard to the formation of spin spirals, and find a crossover to commensurate phases as $U$ increases and a full gap opens. The results are compared with a variety of other recent calculations, and in general good agreement is found. For parameters appropriate to the cuprates, double occupancy should be only mildly suppressed in the absence of magnetic order, inconsistent with a strong-coupling scenario.

arXiv:1207.5538Physical Review BJan 13, 201017 citations

Ground-state phase diagram of the repulsive SU(3) Hubbard model in the Gutzwiller approximation

Ákos Rapp, Achim Rosch

We perform a variational Gutzwiller calculation to study the ground state of the repulsive SU(3) Hubbard model on the Bethe lattice with infinite coordination number. We construct a ground-state phase diagram focusing on phases with a two-sublattice structure and find five relevant phases: (1) a paramagnet, (2) a completely polarized ferromagnet, (3) a two-component antiferromagnet where the third component is depleted, (4) a two-component antiferromagnet with a metallic third component (an ``orbital selective'' Mott insulator), and (5) a density-wave state where two components occupy dominantly one sublattice and the last component the other one. First-order transitions between these phases lead to phase separation. A comparison of the SU(3) Hubbard model to the better-known SU(2) model shows that the effects of doping are completely different in the two cases.We perform a variational Gutzwiller calculation to study the ground state of the repulsive SU(3) Hubbard model on the Bethe lattice with infinite coordination number. We construct a ground-state phase diagram focusing on phases with a two-sublattice structure and find five relevant phases: (1) a paramagnet, (2) a completely polarized ferromagnet, (3) a two-component antiferromagnet where the third component is depleted, (4) a two-component antiferromagnet with a metallic third component (an ``orbital selective'' Mott insulator), and (5) a density-wave state where two components occupy dominantly one sublattice and the last component the other one. First-order transitions between these phases lead to phase separation. A comparison of the SU(3) Hubbard model to the better-known SU(2) model shows that the effects of doping are completely different in the two cases.

arXiv:1102.3053Physical Review AMay 3, 201120 citations

Phase Separation in the Extended Hubbard Model at Weak Coupling

P. G. J. van Dongen

The Hubbard model including nearest-neighbor interaction is studied at $T=0$ on a $d$ -dimensional hypercubic lattice ($d\ensuremath{\ge}3$) close to half filling. It is shown that the ground state at weak coupling is phase separated, consisting of homogeneous lower-density and antiferromagnetic or charge density wave higher-density regions. Incommensurate phases are unstable. The exact critical doping level and the exact order parameter are renormalized relative to the Hartree results. The renormalization factor at weak coupling turns out to be identical to the result found previously for the same model at half filling.The Hubbard model including nearest-neighbor interaction is studied at $T=0$ on a $d$-dimensional hypercubic lattice ($d\ensuremath{\ge}3$) close to half filling. It is shown that the ground state at weak coupling is phase separated, consisting of homogeneous lower-density and antiferromagnetic or charge density wave higher-density regions. Incommensurate phases are unstable. The exact critical doping level and the exact order parameter are renormalized relative to the Hartree results. The renormalization factor at weak coupling turns out to be identical to the result found previously for the same model at half filling.

Physical Review LettersJan 2, 199542 citations

{\mathit{U}}_{\mathit{c}}

/t\ensuremath{\approxeq}2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at

{\mathit{U}}_{\mathit{c}}

=0.

We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (

U

) and nearest-neighbor (

V

) repulsions. For

d

-dimensional hypercubic lattices, when

2\mathit{dV}<U

, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when

2\mathit{dV}>U

, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.

We calculate the magnetic phase diagram of the half-filled $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model as a function of ${t}^{\ensuremath{'}}$ and

U

, within the Gutzwiller approximation plus random-phase approximation. As

U

increases, the system first crosses over to one of a wide variety of incommensurate phases, whose origin is clarified in terms of double nesting. We evaluate the stability regime of the incommensurate phases by allowing for symmetry breaking with regard to the formation of spin spirals, and find a crossover to commensurate phases as

U

increases and a full gap opens. The results are compared with a variety of other recent calculations, and in general good agreement is found. For parameters appropriate to the cuprates, double occupancy should be only mildly suppressed in the absence of magnetic order, inconsistent with a strong-coupling scenario.

The Hubbard model including nearest-neighbor interaction is studied at

T=0

on a

d

-dimensional hypercubic lattice ($d\ensuremath{\ge}3$) close to half filling. It is shown that the ground state at weak coupling is phase separated, consisting of homogeneous lower-density and antiferromagnetic or charge density wave higher-density regions. Incommensurate phases are unstable. The exact critical doping level and the exact order parameter are renormalized relative to the Hartree results. The renormalization factor at weak coupling turns out to be identical to the result found previously for the same model at half filling.