Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1007.0608 · Europhysics Letters (EPL)

Entanglement renormalization of anisotropic XY model

M. Q. Weng

Published Dec 1, 2010• 2 citations
arXivHTMLPDF

Abstract

The renormalization group flows of the one-dimensional anisotropic XY model are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized disentangler removes the short-range entanglement by rotating the system in the parameter space spanned by the anisotropy and the magnetic field. It is understood from the study that the disentangler reduces the entanglement by mapping the system to another one in the same universality class but with smaller short-range entanglement. The phase boundary and corresponding critical exponents are calculated using different schemes with different block sizes, look-ahead steps and truncation dimensions. It is shown that a larger truncation dimension leads to more accurate results and that using a larger block size or look-ahead step improves the overall calculational consistency.

DOI
10.1209/0295-5075/92/60005

Related papers

Quantum renormalization group of the XY model in two dimensions

M. Usman, Asif Ilyas, Khalid Khan

We investigate entanglement and quantum phase transition in a two-dimensional Heisenberg anisotropic spin-$1/2\mathit{XY}$ 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.

arXiv:1708.03365•Physical Review A•Sep 28, 2015•34 citations

Entanglement and quantum phase transition in the one-dimensional anisotropic XY model

Fu-Wu Ma, Sheng-Xin Liu, Xiang-Mu Kong

In this paper the entanglement and quantum phase transition of the anisotropic spin-$1/2$ $\mathit{XY}$ model are studied by using the quantum renormalization-group method. By solving the renormalization equations, we get the trivial and nontrivial fixed points, which correspond to the phase of the system and the critical point, respectively. The concurrence between two blocks are calculated and it is found that when the number of iterations of the renormalization tends to infinity, the concurrence develops two saturated values that are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence and find that there exists nonanalytic behaviors at the quantum critical point, which are directly associated with the divergence of the correlation length. To gain further insight, the scaling behaviors of the system are analyzed and it is shown that the maximum value of the first derivative of the concurrence reaches infinity and the critical point is approached as the size of the system increases.

arXiv:1105.1671•Physical Review A•Jun 7, 2011•86 citations

A new renormalization approach to the ground state of the anisotropic XY model

Raf Dekeyser, A. Drzewiński, J. M. J. van Leeuwen

The renormalization scheme recently proposed by White is applied to the d=1 anisotropic XY model in a transverse field (AXY). A flow diagram, critical exponents and energies have been calculated. It is found that this scheme is a distinct improvement over the standard technique as far as the computation of the ground state is concerned. The accuracy increases rapidly, when we keep more states in each renormalization step, but the errors in the ground state energy are always the largest in the neighborhood of the phase transitions. Comparing with the Ising model in a transverse field, on account of more complicated symmetries, the AXY demands more precautions during constructing a renormalization group transformation.

Acta Physica Slovaca Reviews and Tutorials•Jan 1, 1994•0 citations

Quantum phase transition and entanglement in XXZ Heisenberg spin chain

N. Hachem, El Mostafa Jalal, M. Salama +2 more

Abstract Using the quantum renormalization group approach, we have investigated the entanglement and critical behavior of an anisotropic XXZ Heisenberg spin chain. The resolution of the quantum renormalization equations yields stable and unstable fixed points, corresponding respectively to the phases and critical point of the system. It is shown that a quantum phase transition exists at a critical anisotropy parameter , separating the Néel phase from the spin-fluid phase. Then, the concurrence between two blocks of sites and the quantum coherence have been calculated and presented for various renormalization group iterations. In the thermodynamic limit, i.e. , for higher renormalization steps, the concurrence and coherence exhibit two different saturated values in the two regions separated by Δ c . The first derivative of concurrence diverges at the critical point as the size of the chain increases, showing nonanalytic behavior. Moreover, the scaling behavior has been examined near the critical point with some universal exponential scaling laws.

Europhysics Letters (EPL)•May 21, 2025•6 citations

Entanglement Renormalization

Guifré Vidal

We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.

arXiv:cond-mat/0512165•Physical Review Letters•Nov 28, 2007•1,122 citations

Critical exponents with a multiscale entanglement renormalization Ansatz channel

Simone Montangero, Matteo Rizzi, Vittorio Giovannetti +1 more

We show how to compute the critical exponents of one-dimensional quantum critical systems in the thermodynamic limit. The method is based on an iterative scheme applied to the multiscale entanglement renormalization Ansatz for the ground-state wave function. We test this scheme to compute the critical exponents of the Ising and $XXZ$ model for which we can compare the method with the exact values. The agreement is at worst within few percent of the exact results already for moderate dimensions of the tensor indices.

arXiv:0810.1414•Physical Review B•Sep 30, 2009•28 citations
The renormalization group flows of the one-dimensional anisotropic XY model are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized disentangler removes the short-range entanglement by rotating the system in the parameter space spanned by the anisotropy and the magnetic field. It is understood from the study that the disentangler reduces the entanglement by mapping the system to another one in the same universality class but with smaller short-range entanglement. The phase boundary and corresponding critical exponents are calculated using different schemes with different block sizes, look-ahead steps and truncation dimensions. It is shown that a larger truncation dimension leads to more accurate results and that using a larger block size or look-ahead step improves the overall calculational consistency.
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.
In this paper the entanglement and quantum phase transition of the anisotropic spin-1/21/21/2 XY\mathit{XY}XY model are studied by using the quantum renormalization-group method. By solving the renormalization equations, we get the trivial and nontrivial fixed points, which correspond to the phase of the system and the critical point, respectively. The concurrence between two blocks are calculated and it is found that when the number of iterations of the renormalization tends to infinity, the concurrence develops two saturated values that are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence and find that there exists nonanalytic behaviors at the quantum critical point, which are directly associated with the divergence of the correlation length. To gain further insight, the scaling behaviors of the system are analyzed and it is shown that the maximum value of the first derivative of the concurrence reaches infinity and the critical point is approached as the size of the system increases.
The renormalization scheme recently proposed by White is applied to the d=1 anisotropic XY model in a transverse field (AXY). A flow diagram, critical exponents and energies have been calculated. It is found that this scheme is a distinct improvement over the standard technique as far as the computation of the ground state is concerned. The accuracy increases rapidly, when we keep more states in each renormalization step, but the errors in the ground state energy are always the largest in the neighborhood of the phase transitions. Comparing with the Ising model in a transverse field, on account of more complicated symmetries, the AXY demands more precautions during constructing a renormalization group transformation.
Abstract Using the quantum renormalization group approach, we have investigated the entanglement and critical behavior of an anisotropic XXZ Heisenberg spin chain. The resolution of the quantum renormalization equations yields stable and unstable fixed points, corresponding respectively to the phases and critical point of the system. It is shown that a quantum phase transition exists at a critical anisotropy parameter , separating the Néel phase from the spin-fluid phase. Then, the concurrence between two blocks of sites and the quantum coherence have been calculated and presented for various renormalization group iterations. In the thermodynamic limit, i.e. , for higher renormalization steps, the concurrence and coherence exhibit two different saturated values in the two regions separated by Δ c . The first derivative of concurrence diverges at the critical point as the size of the chain increases, showing nonanalytic behavior. Moreover, the scaling behavior has been examined near the critical point with some universal exponential scaling laws.
We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.
We show how to compute the critical exponents of one-dimensional quantum critical systems in the thermodynamic limit. The method is based on an iterative scheme applied to the multiscale entanglement renormalization Ansatz for the ground-state wave function. We test this scheme to compute the critical exponents of the Ising and XXZXXZXXZ model for which we can compare the method with the exact values. The agreement is at worst within few percent of the exact results already for moderate dimensions of the tensor indices.