Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field

Zarei, Mohammad Hossein

doi:10.1103/physrevb.100.125159

Cited by 17 publications

(9 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, recently the X-cube model in presence of a magnetic field has been studied [39] where a first-order quantum phase transition is identified by a discontinuity in the first derivation of the ground state energy. The first-order nature of phase transition in this model reveals its difference with topological phases such as toric code model which shows a second-order phase transition in presence of a parallel magnetic field [40][41][42].…”

Section: Introductionmentioning

confidence: 83%

“…First, since fracton phases have wave functions with a non-local nature similar to topological phases, we expect that there is a non-local order parameter which is able to characterize phase transition in fracton models. In particular, since order parameters contain all important information about their corresponding phases, it is important to find how the specific features of the fracton phases reveal in a possible non-local order parameter [41]. Second, it is known that phase transitions can be characterized by measures of quantum information theory such as fidelity and entanglement [43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Foliated order parameter in a fracton phase transition

Zarei,

Nobakht

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Finding suitable indicators for characterizing quantum phase transitions plays an important role in understanding different phases of matter. It is especially important for fracton phases where a combination of topology and fractionalization leads to exotic features not seen in other known quantum phases. In this paper, we consider the above problem by studying phase transition in the X-cube model in the presence of a non-linear perturbation. Using an analysis of the ground state fidelity and identifying a discontinuity in the global entanglement, we show there is a firstorder quantum phase transition from a type I fracton phase with a highly entangled nature to a magnetized phase. Accordingly, we conclude that the global entanglement, as a measure of the total quantum correlations in the ground state, can well capture certain features of fracton phase transitions. Then, we introduce a non-local order parameter in the form of a foliated operator which can characterize the above phase transition. We particularly show that such an order parameter has a geometric nature which captures specific differences of fracton phases with topological phases. Our study is specifically based on a well-known dual mapping to the classical plaquette Ising model where it shows the importance of such dualities in studying different quantum phases of matter.

show abstract

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Foliated order parameter in a fracton phase transition

Zarei,

Nobakht

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, we compare the non-local string correlation operators S γ = e∈γ σ z e of our variational states which could be viewed as a measure of the correlation of a pair of excited particle and anti-particle along a path γ. In the topological order phase the non-local string operators will decay to zero while they will remain constant at the trivial phase [53]. In Fig.…”

Section: B 2d Zn Gauge Theorymentioning

confidence: 93%

Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

Luo¹,

Chen²,

Hu³

et al. 2021

Preprint

View full text Add to dashboard Cite

Gauge invariance plays a crucial role in quantum mechanics from condensed matter physics to high energy physics. We develop an approach to constructing gauge invariant autoregressive neural networks for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries. We variationally optimize our gauge invariant autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We exactly represent the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We simulate the dynamics of the quantum link model of U(1) lattice gauge theory, obtain the phase diagram for the 2D Z2 gauge theory, determine the phase transition and the central charge of the SU(2) 3 anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.

show abstract

“…Here, we study TQPT in a perturbed version of the Kitaev Toric code model [38]. The Toric code has been studied in the presence of different types of perturbations where TQPT points are also important as a measure of the robustness of the topological phase against perturbations [39][40][41][42][43][44]. The critical behavior in different quantities including ground-state fidelity [45,46], quantum discord [47], and quantum Fisher information [48] has been studied.…”

Section: Introductionmentioning

confidence: 99%

Global entanglement in a topological quantum phase transition

Samimi,

Zarei,

Montakhab

2022

Preprint

Self Cite

View full text Add to dashboard Cite

A useful approach to characterize and identify quantum phase transitions lies in the concept of multipartite entanglement. In this paper, we consider well-known measures of multipartite (global) entanglement, i.e., average linear entropy of one-qubit and two-qubit reduced density matrices, in order to study topological quantum phase transition (TQPT) in the Kitaev Toric code Hamiltonian with a nonlinear perturbation. We provide an exact mapping from aforementioned measures in the above model to internal energy and energy-energy correlations in the classical Ising model. Accordingly, we find that the global entanglement shows a continuous and sharp transition from a maximum value in the topological phase to zero in the magnetized phase in a sense that its first-order derivative diverges at the transition point. In this regard, we conclude that not only can the global entanglement serve as a reasonable tool to probe quantum criticality at TQPTs, but it also can reveal the highly entangled nature of topological phases. Furthermore, we also introduce a conditional version of global entanglement which becomes maximum at the critical point. Therefore, regarding a general expectation that multipartite entanglement reaches maximum value at the critical point of quantum many-body systems, our result proposes that the conditional global entanglement can be a good measure of multipartite entanglement in TQPTs.

show abstract

Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field

Cited by 17 publications

References 50 publications

Foliated order parameter in a fracton phase transition

Foliated order parameter in a fracton phase transition

Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

Global entanglement in a topological quantum phase transition

Contact Info

Product

Resources

About