arXiv subjects

M. Sanz

Publications and source records attributed to M. Sanz.

40 records · Page 3Linked to original sources

arXiv2009

A canonical form for Projected Entangled Pair States and applications

We show that two different tensors defining the same translational invariant injective Projected Entangled Pair State (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective.

quant-ph↗

arXiv2009

Matrix Product States: Symmetries and Two-Body Hamiltonians

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.

cond-mat.str-el↗

arXiv2008

String order and symmetries in quantum spin lattices

We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection is established, we provide a complete characterization of local symmetries in these states. The results allow to understand in a straightforward way many of the properties of string order parameters, like their robustness/fragility under perturbations and their typical disappearance beyond strictly one-dimensional lattices. We propose and discuss an alternative definition, ideally suited for detecting phase transitions, and generalizations to two and more spatial dimensions.

cond-mat.str-el↗

arXiv2002

Wedge - Shaped Absorbing Samples Look Left Handed: The Problem of Interpreting Negative Refraction, and its Solution

We report experiments of light transmissivity at wavelengths: 532 and 400 nm, through an Au film with a wedge shape. Our results mimic the negative refraction reported by others for so-called left handed materials. A mimic of negative refraction is observed, even though this medium is well known to be right handed, and thus its refractive index has a positive real part. Analogous results are obtained with a glass wedge at 320nm where absorption dominates. The experiment is explained by the wave losses that dominate over propagation, like in the observation of negative refraction, already reported in developed metamaterial wedges. We design and propose an experiment with metamaterials by using thicker wires, in correspondence with light experiments that should conclusively determine whether refraction is positive or negative.

cond-mat↗