DMRG studies of critical SU(N) spin chains

Führinger, M.; Rachel, Stephan; Thomale, Ronny; Greiter, Martin; Schmitteckert, Peter

doi:10.1002/andp.200810326

Cited by 68 publications

(66 citation statements)

References 44 publications

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“…Another family of integrable models has been discovered in the early eighties in which the ground state is also critical [6,7], but the low energy field theory is the SU (2) k=2S Wess-Zumino-Witten model [8], with central charge c = 3k/(2 + k) [9]. These two classes of model have been later on shown to belong to a single, more general family of integrable SU (N ) models with higher symmetric representations [10,11], with a low-energy sector described by the SU (N ) k Wess-Zumino-Witten model, where k is the rank of the symmetric irreducible representation of SU (N ), as shown with Bethe ansatz [12] and confirmed numerically [13]. In both classes, the Hamiltonian contains higher powers of S i · S i+1 with significant coefficients, and the possibility to realize them in actual spin chains is quite remote.…”

Section: Introductionmentioning

confidence: 63%

Realization of higher Wess-Zumino-Witten models in spin chains

Michaud

Manmana²,

Mila³

2013

Phys. Rev. B

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Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (Si−1 · Si)(Si · Si+1) + H.c., we use densitymatrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S = 1, 3/2 and 2. The resulting central charge and critical exponent are in good agreement with the SU (2) k=2S Wess-Zumino-Witten values c = 3k/(2 + k) and η = 3/(2 + k). Since the 3-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU (2) k>1 Wess-Zumino-Witten models might finally be realized in actual spin chains.

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Section: Introductionmentioning

confidence: 63%

Realization of higher Wess-Zumino-Witten models in spin chains

Michaud

Manmana²,

Mila³

2013

Phys. Rev. B

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“…These findings can be further generalized to SU(N ), SP(N ), or SO(N )-symmetric WZW models; for instance, we expect that πvχ = k(N 2 − 1)/6 for SU(N ) k WZW models [114,115] but leave this topic for future work.…”

Section: Extension To Cfts With a Conserved U(1) Chargementioning

confidence: 77%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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“…The results presented in parentheses are some of the best estimates known in the literature (see also Refs. [37][38][39][40][41][42] for similar estimates). As we can see, our estimates are in perfect agreement with those results.…”

mentioning

confidence: 72%

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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DMRG studies of critical SU(N) spin chains

Cited by 68 publications

References 44 publications

Realization of higher Wess-Zumino-Witten models in spin chains

Realization of higher Wess-Zumino-Witten models in spin chains

Bipartite fluctuations as a probe of many-body entanglement

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

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