Quantum phase transitions in multileg spin ladders with ring exchange

Capponi, Sylvain; Lecheminant, P.; Moliner, M.

doi:10.1103/physrevb.88.075132

Cited by 36 publications

(43 citation statements)

References 94 publications

(196 reference statements)

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“…We have not investigated in details the transition between these phases, but their locations are in excellent agreement with the weak-coupling predictions (i.e., U 2 = 0 and U 1 = U 2 ). Moreover, using block entanglement entropy scaling at the transition, one can obtain an estimate of the central charge [123,124], estimated to be 1.8 (on L = 64 chain with U 1 = U 2 = −8t, for instance, data not shown), rather close to the expected c = 2 behavior discussed in Appendix D.…”

Section: B N = 2 P-band Modelmentioning

confidence: 84%

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

et al. 2015

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We investigate possible realizations of exotic SU(N ) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of twoorbital generalizations of the standard SU(N ) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (nondegenerate, charge-density wave, or spin-Peierls-like), we also identify, for even N , two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-N/2 Haldane phase, and a topological SU(N ) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the SU(N ) topological phases found here.

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Section: B N = 2 P-band Modelmentioning

confidence: 84%

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

et al. 2015

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“…Following Ref. 31, we defined the reduced entanglement entropyS N (n) as the one with removed Friedel oscillations:…”

Section: A Triple Pointmentioning

confidence: 99%

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

2016

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We report on a detailed investigation of the spin-1 J1 − J2 − J3 Heisenberg model, a frustrated model with nearest-neighbor coupling J1, next-nearest neighbor coupling J2, and a three site interaction J3 [(Si−1 · Si)(Si · Si+1) + H.c.] previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the SU (2)2 Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the SU (2)2 transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.

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“…Although the DMRG is based on a one-dimensional algorithm, it has been applied to low-dimensional systems such as the ladder system [2]. The procedure consists in mapping the low-dimensional model on a 1D model with long-range interactions [3][4][5][6][7][8][9][10][11][12][13][14][15]. In this vein some other algorithms, based on the tensor networks, have been proposed to study strongly correlated systems in dimensions higher than d = 1, such as projected entangled pair state [16] and multiscale entanglement renormalization ansatz [17].…”

Section: Introductionmentioning

confidence: 99%

N-leg spin-SHeisenberg ladders: A density-matrix renormalization group study

Ramos

Xavier

2014

Phys. Rev. B

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We investigate the N -leg spin-S Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap s and of the ground-state energy per site e N ∞ in the thermodynamic limit for ladders with widths up to six legs and spin S 5 2 . We also estimate the ground-state energy per site e 2D ∞ for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for N odd and gapped for N even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with N odd, similar to what happens in spin chains.

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Quantum phase transitions in multileg spin ladders with ring exchange

Cited by 36 publications

References 94 publications

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

N-leg spin-SHeisenberg ladders: A density-matrix renormalization group study

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