All rights reserved. We first review the Klein bottle entropy in rational CFT and discuss details of how to extract the Klein bottle entropy from lattice models using the example of the transverse field Ising model. [1] The Jordan-Wigner Transformation solves the 1D XY model by mapping spins to fermions. Rev. I��e)�)߿�����'UNqE1� This Letter opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena. Ni�u��`����_�:/f���oA�@D/�?�+�k����ew�?.����IH��l`R�s�� �(�jr.G�S J��g���`�҉=d� w�x�i� �b� �ɳ��V���'���@��P������$�����іH�)+���}��\ �|о������}d%l|���K��,��&,U=-�u U;��EG#1�:�Yױ����Z�:�;��2��q0�DLc�̿�9��.c#*�'�gX��2���c�=�@B���>���ׇ��cu���'m�hw����AVV�MC�����%~ �D�L�X��b�~Ԕ�����n�8��?u�͠(�v��;nm÷'�kܣ�������B�e?� M�$a-���^ The eta-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [Phys. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Néel and dimer-Néel). The resulting quantum many-body scars are therefore of novel origin. Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction Ben-Qiong Liu, 1 Bin Shao, 1* Jun-Gang Li, Jian Zou, 1 and Lian-Ao Wu2 1 Key Laboratory of Cluster Science of Ministry of Education, and Department of Physics, Beijing Institute of Technology, Beijing 100081, China α ranges from 0 to 1, which are the limits of XY and Ising models, respectively. There we also highlight another (orthogonal) tower of exact eigenstates that arise for PBC and D = 0 in d = 1. Lett. This dynamics can be completely understood in terms of the evolution of entangled virtual spin-1/2 degrees of freedom, which in turn underpin the presence of an extensive tower of strong-eigenstate thermalization hypothesis (ETH)-violating many-body eigenstates. While generic initial states are expected to thermalize, we show analytically that the eigenstates we construct lead to weak ergodicity breaking in the form of persistent oscillations of local observables following certain quantum quenches—in other words, these eigenstates provide an archetypal example of so-called quantum many-body scars. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Lett. We elucidate the transition between two different planar phases at large negative D. The low-temperature properties of the spin-S quantum spin chain are studied representing a spin-S operator as the sum of 2S spin-1/2 operators. The phase diagram of the 1D, argument can be applied for the random coupling case. M���`�!�|3m� &ͮ��v������kr��9�+#����=nEk�4�>�q��J�$�p�m���s��� ���g}��{)"�d����.�Os�B�b��P,&L-_�q�{~n��G�#�#9=!T��-1���-�F�E�(Q��q�~!D��^��SXp,�HFQ�D�?�Woe5��'Tf�����lȇ%�t��2�{� n���������ߜ��QKF. Rev. We use cookies to help provide and enhance our service and tailor content and ads. Finite-cell calculations (up to N=12 spins) have been performed on the spin-1 Heisenberg-Ising chain with an uniaxial anisotropy, H=Σi[SixSi+1x+SiySi+1y+λSizSi+1z+D(Siz)2]. The Haldane conjecture suggests a fundamental difference between half-integer and integer antiferromagnetic Heisenberg spin chains. It is shown that under scaling, the coupling becomes strong. Numerical finite-size-scaling results confirm this. Model and phase diagram We consider a 1D spin1/2 XY model in a transverse magnetic With this method, in order k - 1 to determine the BKT critical point, we can use the level crossing of the lower excitations instead of those for the periodic boundary case, thus the convergence to the transition point is highly improved. All content in this area was uploaded by Kiyohide Nomura on Feb 15, 2015. For d = 1 and OBC, H also has a nonlocal SU(2) symmetry. We study the spin-1 XY model on a hypercubic lattice in d dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors. This model is appropriate to study the VBS picture and hidden Z2×Z2 symmetry concerning to the Haldane gap problem. Problem 1: One-dimensional XY model Consider XY model in one dimension described by E = −J P j cos(φ j −φ j+1). They differ only in the mathematical formulation of broken symmetry in the spin representation. We also discuss similarities between the η-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. ... Now, through a lengthy but straightforward calculation as shown in Ref. Stability results Exact non-local NRBCs were introduced in the 1980s. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Rev. Universal scaling relations between exponents for transverse and longitudinal correlations in the phases XY1 and XY2 and an explicit asymptotic expression for correlation functions are derived. Access scientific knowledge from anywhere. It is shown that these eigenstates are metastable and possess an energy gap. The 1D Ising model does not have a phase transition. recently high-order local NRBCs have been devised. 7Lq��& We use periodic, twisted, and open boundary conditions. This content has been downloaded from IOPscience. The strict error estimation is established. (http://iopscience.iop.org/0305-4470/36/23/104), View the table of contents for this issue, or go to the journal homepage for more, of [2–5] argued that the above mentioned degeneracies at the, These operators satisfy the commutation relation, Let us see the commutativity of the operator, of degenerate states for the periodic and th, it is a degenerate eigenstate of the Hamiltonian.

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