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Physica Scripta

Behavior of quantum coherence in quantum phase transitions of two-dimensional XY and ising models

Narjes Taghadomi, Azam Mani, Ali Bakouei

Published Apr 18, 2024• 0 citations
Publisher

Abstract

Abstract We investigate the quantum coherence behavior of the ground states of 2D Heisenberg XY model and 2D Ising model with a transverse field on square lattices using the Quantum Renormalization Group (QRG) method. Our analysis focused on the ground state density matrix and its marginal states, revealing non-analytic behavior of quantum coherence (especially two-site coherence) near the critical point. This behavior allowed us to detect quantum phase transitions (QPT) in these models. By examining the scaling behavior of the maximum derivative of quantum coherence with system size, we determined the critical exponent of coherence for both models and the length exponent of the Ising model. Additionally, we investigated the time evolution of coherence in both models. Our results closely align with those obtained from entanglement analysis, that is while quantum coherence requires fewer computational calculations compared to discord and entanglement approaches.

DOI
10.1088/1402-4896/ad4060

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•Sep 16, 2015•0 citations
Abstract We investigate the quantum coherence behavior of the ground states of 2D Heisenberg XY model and 2D Ising model with a transverse field on square lattices using the Quantum Renormalization Group (QRG) method. Our analysis focused on the ground state density matrix and its marginal states, revealing non-analytic behavior of quantum coherence (especially two-site coherence) near the critical point. This behavior allowed us to detect quantum phase transitions (QPT) in these models. By examining the scaling behavior of the maximum derivative of quantum coherence with system size, we determined the critical exponent of coherence for both models and the length exponent of the Ising model. Additionally, we investigated the time evolution of coherence in both models. Our results closely align with those obtained from entanglement analysis, that is while quantum coherence requires fewer computational calculations compared to discord and entanglement approaches.
We investigate the behavior of quantum coherence of the ground states of 2D Heisenberg XY model and 2D Ising model with transverse field on square lattices, by using the method of Quantum Renormalization Group (QRG). We show that the non-analytic behavior of quantum coherence near the critical point, can detect quantum phase transition (QPT) of these models. We also use the scaling behavior of maximum derivative of quantum coherence, with system size, to find the critical exponent of coherence for both models and also the length exponent of the Ising model. The results are in close agreement with the ones obtained from entanglement analysis, that is while quantum coherence needs less computational calculations in comparison to entanglement approaches.
By using quantum renormalization group (QRG) approach, we first derive the effective Hamiltonian and QRG equations of the two-dimensional (2D) Ising models with two different time-dependent transverse magnetic fields analytically. Then we examine the nonanalytic and scaling behaviors of the linear-entropy-based uncertainty relation and quantum entanglement of the models near the critical point through numerical analysis. Moreover, we investigate the relation between the quantum critical point and the external magnetic field. Our results show that both the uncertainty relation and the quantum entanglement are feasible to detect the quantum phase transition (QPT), and the uncertainty relation may be a better indicator of QPT than quantum entanglement. Our findings could shed new light on the observable of the QPTs of the solid-state system with the uncertainty relation.
We investigate entanglement and quantum phase transition in a two-dimensional Heisenberg anisotropic spin-1/2XY1/2\mathit{XY}1/2XY model, using the quantum renormalization-group method (QRG) on a square lattice of $N\ifmmode\times\else\texttimes\fi{}N$ sites. The entanglement through geometric average of concurrences is calculated after each step of the QRG. We show that the concurrence achieves a nonzero value at the critical point more rapidly as compared to the one-dimensional case. The relationship between the entanglement and the quantum phase transition is studied. The evolution of entanglement develops two saturated values corresponding to two different phases. We compute the derivative of the concurrence, which is found to be discontinuous at the critical point $\ensuremath{\gamma}=0$, and indicates a second-order phase transition in the spin system. Further, the scaling behavior of the system is investigated by computing the derivative of the concurrence in terms of the system size.
We use the quantum renormalization-group (QRG) method to study the entanglement and quantum phase transition (QPT) in the one-dimensional spin-1/2 Heisenberg—Ising model [Lieb E, Schultz T and Mattis D 1961 Ann. Phys. (N.Y.) 16 407]. We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations. We also investigate the scaling behavior of the system close to the quantum critical point, which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size. Also, the first derivative of concurrence between two blocks diverges at the quantum critical point, which is directly associated with the divergence of the correlation length.
We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpiński fractal lattices by employing the multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of the multipartite entanglement and quantum coherence exhibit singular behaviors, and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpiński fractal lattices. Furthermore, the dimensions determine the relations between the critical exponents and the correlation length exponents for these lattices.
We study the ground state quantum correlation of Ising model in a transverse field by implementing the quantum renormalization group (QRG) theory. It is shown that various quantum correlation measures and the Clauser-Horne-Shimony-Holt inequality will highlight the critical point related with quantum phase transitions, and demonstrate nonanalytic phenomenon and scaling behavior when the size of the system becomes large. Our results also indicate a universal behavior of the critical exponent of Ising model under QRG that the critical exponent will not change with the variation of different quantities, even when the quantities vary from entanglement measures to quantum correlation measures. This means that the two kinds of quantum correlation criterion, including the entanglement/separability paradigm and the information-theoretic paradigm, have some connections between them. These remarkable behaviors may have important implications on condensed matter physics because the critical exponent directly associates with the correlation length exponent.