Stripes in the two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi></mml:math>model with infinite projected entangled-pair states

Corboz, Philippe; White, Steven R.; Vidal, G.; Troyer, Matthias

doi:10.1103/physrevb.84.041108

Cited by 198 publications

(194 citation statements)

References 41 publications

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“…The main question in this context is whether the ground state is homogeneous with the possible signatures of d-wave pairing [9,10] or it possesses inhomogeneous state, e.g., phase separation [11] or stripe order [12]. So far, no agreement on this issue has been reached yet.…”

Section: Introductionmentioning

confidence: 88%

Two Holes in the t–J Model Form a Bound State for Any Nonzero J/t

Vidmar

Bonča

2013

J Supercond Nov Magn

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Determination of the parameter regime in which two holes in the t-J model form a bound state represents a long standing open problem in the field of strongly correlated systems. By applying and systematically improving the exact diagonalization method defined over a limited functional space (EDLFS), we show that the average distance between two holes scales as d ∼ 2(J/t) −1/4 for J/t < 0.15, therefore providing strong evidence that two holes in the t-J model form the bound state for any nonzero J/t. However, the symmetry of such bound pair in the ground state is p-wave. This state is consistent with phase separation at finite hole filling, as observed in a recent study [Maska et al, Phys. Rev. B 85, 245113 (2012)].

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Section: Introductionmentioning

confidence: 88%

Two Holes in the t–J Model Form a Bound State for Any Nonzero J/t

Vidmar

Bonča

2013

J Supercond Nov Magn

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“…Nevertheless these results indicate that from the point of view of local energetics the PDW state is very competitive and would most likely be the ground state for some extension of the Hamiltonians that were studied. A very recent and numerically intensive calculation using infinite projected entangled pair states (an extension of the density matrix renormalization group) by Corboz et al 28 have found stripe states coexisting with superconductivity in the 2D t − J model but has not yet investigated the presence (or absence) of a PDW state.…”

Section: Introductionmentioning

confidence: 99%

Pair-density-wave superconducting order in two-leg ladders

Jaefari

Fradkin

2012

Phys. Rev. B

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We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux π per plaquette) have commensurate pair-density wave (PDW) phases. In the case of the conventional (flux-less) ladder the PDW arises when certain filling fractions for which commensurability conditions are met. For the flux π ladder the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase the uniform superconducting order parameter, the 2kF charge-densitywave (CDW) order parameter and the spin-density-wave Néel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi long range order. By making use of bosonization and the renormalization group we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the KondoHeisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.

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“…The accuracy of the iPEPS can be systematically controlled by the so-called bond dimension D. Details on the method can be found in refs. [4,5].Figure 1(a) shows an example of a jump in n(µ) for V = 1.72 between the two densities n 1 ≈ 0.11 and n 2 ≈ 0.89 obtained with iPEPS. For densities in between these two values there is no stable homogenous solution, because it is energetically favorable for the system to split into two regions, one with density n 1 and the other one with n 2 .…”

mentioning

confidence: 99%

“…The accuracy of the iPEPS can be systematically controlled by the so-called bond dimension D. Details on the method can be found in refs. [4,5].…”

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confidence: 99%

Comment on “Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice” by Poletti D. et al.

Corboz¹,

Capponi²,

Läuchli³

et al. 2012

EPL

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In a recent letter [1] a model of attractive spinless fermions on the honeycomb lattice at half filling has been studied by mean-field theory, where distinct homogenous phases at rather large attraction strength V > 3.36, separated by (topological) phase transitions, have been predicted. In this comment we argue that without additional interactions the ground states in these phases are not stable against phase separation. We determine the onset of phase separation at half filling V ps ≈ 1.7 by means of infinite projected entangled-pair states (iPEPS) [2][3][4] and exact diagonalization (ED).The Hamiltonian of the model readŝ(1) with t = 1 the hopping amplitude, and V > 0 the attraction strength. We work in the grand-canonical ensemble, i.e. we use a chemical potential µ to control the particle density n(µ) in the system. Setting µ = 0 corresponds to a half-filled state, n = 0.5, if the state at half filling is stable towards phase separation.Intuitively, at half filling, if the attraction V is much stronger than the hopping t, the fermions can minimize their energy by clustering, leading to phase separation, where half of the system is empty and the other half is occupied by the fermions. In the grand-canonical ensemble, such an instability can be identified as a discontinuity (a jump) in the particle density n(µ) at µ = 0.Figure 1(a) summarizes our numerical results obtained with ED on finite systems and with iPEPS, a tensor network ansatz to simulate the model directly in the thermodynamic limit. The accuracy of the iPEPS can be systematically controlled by the so-called bond dimension D. Details on the method can be found in refs. [4,5].Figure 1(a) shows an example of a jump in n(µ) for V = 1.72 between the two densities n 1 ≈ 0.11 and n 2 ≈ 0.89 obtained with iPEPS. For densities in between these two values there is no stable homogenous solution, because it is energetically favorable for the system to split into two regions, one with density n 1 and the other one with n 2 . Since iPEPS is an ansatz for a homogeneous phase, we either obtain a state with density n 1 or a state with density n 2 for µ = 0, if there is no homogenous solution at half filling. For very large attraction, V 1.9, the system splits into a completely empty and a completely filled region, i.e. n 1 = 0, n 2 = 1. The dependence of n 1 as a function of V is shown in fig. 1(c).The full symbols in fig. 1(b) for V < 1.71 show the iPEPS energy of stable solutions at half filling for µ = 0, whereas the open symbols for V > 1.71 correspond to states away from half-filling, where the state at half-filling arXiv:1204.4791v1 [cond-mat.str-el]

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Stripes in the two-dimensionalt-Jmodel with infinite projected entangled-pair states

Cited by 198 publications

References 41 publications

Two Holes in the t–J Model Form a Bound State for Any Nonzero J/t

Two Holes in the t–J Model Form a Bound State for Any Nonzero J/t

Pair-density-wave superconducting order in two-leg ladders

Comment on “Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice” by Poletti D. et al.

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