In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two, and three dimensions from a multipartite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric Greenberger-Horne-Zeilinger--like state to a paramagnetic product state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one- and two-dimensional models. Our results indicate that such multipartite measure of global entanglement shows universal features regardless of dimension $d$ . Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two, and three dimensions from a multipartite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric Greenberger-Horne-Zeilinger--like state to a paramagnetic product state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one- and two-dimensional models. Our results indicate that such multipartite measure of global entanglement shows universal features regardless of dimension $d$. Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.

arXiv:1009.1357Physical Review ADec 14, 201040 citations

Quantum phase transitions in the two-dimensional J1−J2 model

Oleg P. Sushkov, J. Oitmaa, Zheng Weihong

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the ${J}_{1}{\ensuremath{-}J}_{2}$ model, in two dimensions. Two quantum phase transitions in the model are already known: the second-order transition from the N\'eel state to the spin liquid state at ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38,$ and the first-order transition from the spin liquid state to the collinear state at ${(J}_{2}{/J}_{1}{)}_{c4}\ensuremath{\approx}0.60.$ We have found evidence for two second-order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette-type modulation at ${(J}_{2}{/J}_{1}{)}_{c3}=0.50\ifmmode\pm\else\textpm\fi{}0.02,$ and the transition from the simple N\'eel state to the N\'eel state with spin columnar dimerization at ${(J}_{2}{/J}_{1}{)}_{c1}=0.34\ifmmode\pm\else\textpm\fi{}0.04.$ We also present an independent calculation of ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38$ using another approach.We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the ${J}_{1}{\ensuremath{-}J}_{2}$ model, in two dimensions. Two quantum phase transitions in the model are already known: the second-order transition from the N\'eel state to the spin liquid state at ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38,$ and the first-order transition from the spin liquid state to the collinear state at ${(J}_{2}{/J}_{1}{)}_{c4}\ensuremath{\approx}0.60.$ We have found evidence for two second-order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette-type modulation at ${(J}_{2}{/J}_{1}{)}_{c3}=0.50\ifmmode\pm\else\textpm\fi{}0.02,$ and the transition from the simple N\'eel state to the N\'eel state with spin columnar dimerization at ${(J}_{2}{/J}_{1}{)}_{c1}=0.34\ifmmode\pm\else\textpm\fi{}0.04.$ We also present an independent calculation of ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38$ using another approach.

arXiv:cond-mat/0007329Physical review. B, Condensed matterFeb 20, 2001151 citations

A study of quantum phase transitions in two dimensional electron systems

Xin Wan

Oct 1, 20001 citation

Evidence for mixed phases and percolation at the metal-insulator transition in two dimensions

Shiqi Li, Qing Zhang, Pouyan Ghaemi +1 more

The in-plane magnetoconductance of the strongly interacting two-dimensional electron system in a silicon MOSFET (metal-oxide-semiconductor-field-effect transistor) exhibits an unmistakable kink at a well-defined electron density, ${n}_{k}$ . The kink at ${n}_{k}$ is near, but not at the critical density ${n}_{c}$ determined from resistivity measurements, and the density at which ${n}_{k}$ occurs varies with temperature. These features are inconsistent with expectations for a quantum phase transition. We suggest instead that this is a percolation transition and present a detailed model based on the formation of a mixed insulating and metallic phase within which a metal-insulator transition takes place by percolation.The in-plane magnetoconductance of the strongly interacting two-dimensional electron system in a silicon MOSFET (metal-oxide-semiconductor-field-effect transistor) exhibits an unmistakable kink at a well-defined electron density, ${n}_{k}$. The kink at ${n}_{k}$ is near, but not at the critical density ${n}_{c}$ determined from resistivity measurements, and the density at which ${n}_{k}$ occurs varies with temperature. These features are inconsistent with expectations for a quantum phase transition. We suggest instead that this is a percolation transition and present a detailed model based on the formation of a mixed insulating and metallic phase within which a metal-insulator transition takes place by percolation.

arXiv:1811.04954Physical review. B./Physical review. BApr 8, 201912 citations

d

. Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.

{n}_{k}

. The kink at

{n}_{k}

is near, but not at the critical density

{n}_{c}

determined from resistivity measurements, and the density at which

{n}_{k}

occurs varies with temperature. These features are inconsistent with expectations for a quantum phase transition. We suggest instead that this is a percolation transition and present a detailed model based on the formation of a mixed insulating and metallic phase within which a metal-insulator transition takes place by percolation.