Crystals of bound states in the magnetization plateaus of the
  Shastry-Sutherland model

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Abstract

Using infinite projected entangled-pair states (iPEPS), we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and {\it not} to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu\(_2\)(BO\(_3\))\(_2\), and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a {\it localized} bound state with \(S_z=2\). Finally, we discuss the role of competing domain-wall and supersolid phases as well as that of additional anisotropic interactions.

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Entanglement in quantum critical phenomena

J. I. Latorre, A. Kitaev, G Vidal … (2002)

Quantum phase transitions occur at zero temperature and involve the appearance of long-range correlations. These correlations are not due to thermal fluctuations but to the intricate structure of a strongly entangled ground state of the system. We present a microscopic computation of the scaling properties of the ground-state entanglement in several 1D spin chain models both near and at the quantum critical regimes. We quantify entanglement by using the entropy of the ground state when the system is traced down to \(L\) spins. This entropy is seen to scale logarithmically with \(L\), with a coefficient that corresponds to the central charge associated to the conformal theory that describes the universal properties of the quantum phase transition. Thus we show that entanglement, a key concept of quantum information science, obeys universal scaling laws as dictated by the representations of the conformal group and its classification motivated by string theory. This connection unveils a monotonicity law for ground-state entanglement along the renormalization group flow. We also identify a majorization rule possibly associated to conformal invariance and apply the present results to interpret the breakdown of density matrix renormalization group techniques near a critical point.

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Classical simulation of infinite-size quantum lattice systems in two spatial dimensions

F. Verstraete, J Cirac, J. Jordan … (2007)

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac, cond-mat/0407066] and the infinite {\em time-evolving block decimation} algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analysing its second order quantum phase transition.

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Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2

Shin Miyahara, Kazuo Ueda (1998)

The two dimensional Heisenberg model for SrCu_2(BO_3)_2 has the exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N\'{e}el ordered state is determined. Analysis of the experimental data shows that SrCu_2(BO_3)_2 has the dimer ground state but is close to the transition point, which leads to the unusual temperature dependence of the susceptibility. Almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.