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:2001.10550 · Physical review. B./Physical review. B

Boundary criticality of topological quantum phase transitions in two-dimensional systems

Xiao-Chuan Wu, Yichen Xu, Hao Geng, Chao‐Ming Jian, Cenke Xu

Published May 5, 2020• 8 citations
arXivHTMLPDF

Abstract

We discuss the boundary critical behaviors of two-dimensional (2D) quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the one-dimensional boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: (i) the quantum phase transition between a 2D ${Z}_{2}$ topological order and an ordered phase with spontaneous symmetry breaking; (ii) the continuous quantum phase transition between metal and a particular type of Mott insulator [$\mathrm{U}(1)$ spin liquid]. In particular, we obtain the critical exponents and scaling laws of these exotic quantum phase transitions when the systems are probed from the boundary in proposed experimental setup. These critical exponents obtained are significantly different from those one would see through bulk measurements. This theoretical study could be relevant to many purely 2D systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.

DOI
10.1103/physrevb.101.174406

Related papers

Boundary criticality in two-dimensional correlated topological superconductors

Ge Yang, Huan Jiang, Hong Yao +1 more

The presence of a boundary enriches the nature of quantum phase transitions. However, the boundary critical phenomena in topological superconductors remain underexplored so far. Here, we investigate the boundary criticality in a two-dimensional correlated time-reversal-invariant topological superconductor tuned through a quantum phase transition into a trivial time-reversal-breaking superconductor. Using sign-problem-free determinant quantum Monte Carlo simulations, we chart the quantum phase diagram and reveal the boundary criticalities encompassing ordinary, special, and extraordinary transitions. Additionally, using renormalization group analysis, we compute the boundary critical exponent up to two loops. Remarkably, the simulations and two-loop renormalization group calculations consistently demonstrate that the presence of the boundary Majorana fermion at the special transition gives rise to a new type of boundary Gross-Neveu-Yukawa fixed point. We conclude with a discussion of possible experimental realizations in iron-based superconductors.

arXiv:2510.05230•Oct 6, 2025•0 citations

Quantum scaling for the metal–insulator transition in a two-dimensional electron system

V. Kagalovsky, S. V. Kravchenko, Demitry Nemirovsky

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase's resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

Scientific Reports•May 31, 2024•4 citations

Boundary criticality in two-dimensional interacting topological insulators

Yang Ge, Hong Yao, Shao-Kai Jian

We study the boundary criticality in 2D interacting topological insulators. Using the determinant quantum Monte Carlo method, we present a nonperturbative study of the boundary quantum phase diagram in the Kane-Mele-Hubbard-Rashba model. Our results reveal rich boundary critical phenomena at the quantum phase transition between a topological insulator and an antiferromagnetic insulator, encompassing ordinary, special, and extraordinary transitions. Combining analytical derivation of the boundary theory with unbiased numerically exact quantum Monte Carlo simulations, we demonstrate that the presence of topological edge states enriches the ordinary transition that renders a continuous boundary scaling dimension and, more intriguingly, leads to a special transition of the Berezinskii-Kosterlitz-Thouless type. Our work establishes a framework for the nonperturbative study of boundary criticality in two-dimensional topological systems with strong electron correlations.

arXiv:2504.12600•Physical review. B./Physical review. B•Feb 23, 2026•1 citation

Boundary and defect criticality in topological insulators and superconductors

Xiaoyang Shen, Zhengzhi Wu, Shao-Kai Jian

We study the boundary criticality enriched by boundary fermions, which ubiquitously emerge in topological phases of matter, with a focus on topological insulators and topological superconductors. By employing dimensional regularization and bosonization techniques, we uncover several unprecedented boundary universality classes. These include the boundary Gross-Neveu-Yukawa critical point and the special Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the interplay between edge modes and bulk bosons. We present a comprehensive sketch of the phase diagram that accommodates these boundary criticalities and delineate their critical exponents. Additionally, we explore a 1+1D conformal defect decorated with fermions, where a defect BKT transition is highlighted. We conclude with a discussion on potential experimental realizations of these phenomena.

arXiv:2407.15916•Physical review. B./Physical review. B•Jun 26, 2025•5 citations

Fractionalized Fermionic Quantum Criticality in Spin-Orbital Mott Insulators

Urban F. P. Seifert, Xiaoyu Dong, Sreejith Chulliparambil +3 more

We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu* universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a t-V model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ ε-expansion and large-N methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with d^{1} electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.

arXiv:2009.05051•Physical Review Letters•Dec 14, 2020•48 citations

Exotic $Z_2$ Symmetry Breaking Transitions in 2D Correlated Systems

Sangjin Lee, Jun Yeong Jung, Ara Go +1 more

The Landau paradigm of phase transitions is one of the backbones in critical phenomena. With a $Z_2$ symmetry, it describes the Ising universality class whose central charge is one half (c = 1=2) in two spatial dimensions (2D). Recent experiments in strongly correlated systems, however, suggest intriguing possibilities beyond the Landau paradigm. We uncover an exotic universality class of a $Z_2$ symmetry breaking transition with c = 1. It is shown that fractionalization of discrete symmetry order parameters may realize the exotic class. In addition to novel critical exponents, we find that the onset of an order parameter may be super-linear in contrast to the sub-linear onset of the Ising class. We argue that a super-linear onset of a $Z_2$ order parameter without breaking a bigger symmetry than $Z_2$ is evidence of exotic phenomena, and our results are applied to recent experiments in phase transitions at pseudo-gap temperatures.

arXiv:1803.00578•Mar 1, 2018•3 citations
We discuss the boundary critical behaviors of two-dimensional (2D) quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the one-dimensional boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: (i) the quantum phase transition between a 2D Z2{Z}_{2}Z2​ topological order and an ordered phase with spontaneous symmetry breaking; (ii) the continuous quantum phase transition between metal and a particular type of Mott insulator [U(1)\mathrm{U}(1)U(1) spin liquid]. In particular, we obtain the critical exponents and scaling laws of these exotic quantum phase transitions when the systems are probed from the boundary in proposed experimental setup. These critical exponents obtained are significantly different from those one would see through bulk measurements. This theoretical study could be relevant to many purely 2D systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.
The presence of a boundary enriches the nature of quantum phase transitions. However, the boundary critical phenomena in topological superconductors remain underexplored so far. Here, we investigate the boundary criticality in a two-dimensional correlated time-reversal-invariant topological superconductor tuned through a quantum phase transition into a trivial time-reversal-breaking superconductor. Using sign-problem-free determinant quantum Monte Carlo simulations, we chart the quantum phase diagram and reveal the boundary criticalities encompassing ordinary, special, and extraordinary transitions. Additionally, using renormalization group analysis, we compute the boundary critical exponent up to two loops. Remarkably, the simulations and two-loop renormalization group calculations consistently demonstrate that the presence of the boundary Majorana fermion at the special transition gives rise to a new type of boundary Gross-Neveu-Yukawa fixed point. We conclude with a discussion of possible experimental realizations in iron-based superconductors.
The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase's resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.
We study the boundary criticality in 2D interacting topological insulators. Using the determinant quantum Monte Carlo method, we present a nonperturbative study of the boundary quantum phase diagram in the Kane-Mele-Hubbard-Rashba model. Our results reveal rich boundary critical phenomena at the quantum phase transition between a topological insulator and an antiferromagnetic insulator, encompassing ordinary, special, and extraordinary transitions. Combining analytical derivation of the boundary theory with unbiased numerically exact quantum Monte Carlo simulations, we demonstrate that the presence of topological edge states enriches the ordinary transition that renders a continuous boundary scaling dimension and, more intriguingly, leads to a special transition of the Berezinskii-Kosterlitz-Thouless type. Our work establishes a framework for the nonperturbative study of boundary criticality in two-dimensional topological systems with strong electron correlations.
We study the boundary criticality enriched by boundary fermions, which ubiquitously emerge in topological phases of matter, with a focus on topological insulators and topological superconductors. By employing dimensional regularization and bosonization techniques, we uncover several unprecedented boundary universality classes. These include the boundary Gross-Neveu-Yukawa critical point and the special Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the interplay between edge modes and bulk bosons. We present a comprehensive sketch of the phase diagram that accommodates these boundary criticalities and delineate their critical exponents. Additionally, we explore a 1+1D conformal defect decorated with fermions, where a defect BKT transition is highlighted. We conclude with a discussion on potential experimental realizations of these phenomena.
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu* universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a t-V model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ ε-expansion and large-N methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with d^{1} electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.
Exotic Z2Z_2Z2​ Symmetry Breaking Transitions in 2D Correlated Systems
The Landau paradigm of phase transitions is one of the backbones in critical phenomena. With a Z2Z_2Z2​ symmetry, it describes the Ising universality class whose central charge is one half (c = 1=2) in two spatial dimensions (2D). Recent experiments in strongly correlated systems, however, suggest intriguing possibilities beyond the Landau paradigm. We uncover an exotic universality class of a Z2Z_2Z2​ symmetry breaking transition with c = 1. It is shown that fractionalization of discrete symmetry order parameters may realize the exotic class. In addition to novel critical exponents, we find that the onset of an order parameter may be super-linear in contrast to the sub-linear onset of the Ising class. We argue that a super-linear onset of a Z2Z_2Z2​ order parameter without breaking a bigger symmetry than Z2Z_2Z2​ is evidence of exotic phenomena, and our results are applied to recent experiments in phase transitions at pseudo-gap temperatures.