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Chinese Physics Letters

Quantum Phase Transitions in Matrix Product States

祝敬敏

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

我们在场与矩阵产品在旋转链系统构造各种各样的量阶段转变(QPT ) 的一个新一般、简单得多的计划扎根了状态。由计划的使用，我们考虑一个种矩阵产品状态(MPS ) QPT 并且提供一个具体模型。我们也学习一种 QPT 出现的具体例子和表演的性质，由同等值的断绝的外观伴随了不在的块仅仅为同等值的物理看得见的、分叉的关联长度不在的块操作员，并且是转变点的固定的点是重正常化的一个孤立的中间联合的固定的点的另外的性质流动并且一半无限的链的纠纷熵是不连续的。[从作者抽象]

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Uspekhi Fizicheskih Nauk•Jan 1, 2003•2 citations
我们在场与矩阵产品在旋转链系统构造各种各样的量阶段转变(QPT ) 的一个新一般、简单得多的计划扎根了状态。由计划的使用，我们考虑一个种矩阵产品状态(MPS ) QPT 并且提供一个具体模型。我们也学习一种 QPT 出现的具体例子和表演的性质，由同等值的断绝的外观伴随了不在的块仅仅为同等值的物理看得见的、分叉的关联长度不在的块操作员，并且是转变点的固定的点是重正常化的一个孤立的中间联合的固定的点的另外的性质流动并且一半无限的链的纠纷熵是不连续的。[从作者抽象]
根据我们到在纺纱的构造量阶段转变(QPT ) 的计划，有矩阵产品的链系统扎根了状态，我们成功地首先把矩阵产品状态(MPS ) QPT 与自发的对称碎相结合。为一个具体模型，我们考虑自发的同等值碎伴随的一种 MPS QPT ，尽管为批评的点的任何一个方面 GS 典型地是唯一的，并且证明 MPS QPT 的类型仅仅在热力学的限制发生并且被奇特，分叉的关联长度，消失的精力差距和一半无限的链的纠纷熵的外观伴随保持有限不仅而且谁的第一衍生物不连续。
A matrix product system chooses a special path in the phase diagram to undergo a quantum phase transition (QPT) and shows different behaviors compared with a traditional QPT, such as the symmetry behavior of some physical observables described in this paper. An equation is established, which (i) helps one to understand the special behaviors of a matrix product state (MPS)-QPTs, and (ii) can be used to detect the QPT point of a MPS, much simpler than usual procedures of calculating the transfer matrix or density matrix of the system. The equation acts as a selection rule for the path of the MPS-QPT and is believed to be the essence of distinguishing a MPS-QPT from a traditional QPT. Furthermore, the discontinuity of the derivative of an observable is found to be connected directly to the turning point in the path of the MPS, but not the phase boundary point in the phase diagram, though the two are in accordance with each other in many cases.
According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.
We present a new general and much simpler scheme to construct various quantum phase transitions (QPTs) in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state (MPS) QPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of QPT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.
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