The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.

arXiv:1508.03646Physical Review LettersJan 14, 201623 citations

Rabi transport and the other finite-size effects in one-dimensional discrete-time topological quantum walk

Andrzej Grudka, Marcin Karczewski, Paweł Kurzyński +3 more

Abstract This paper investigates Rabi transport and finite-size effects in one-dimensional discrete-time topological quantum walks. We demonstrate the emergence of localized states at boundaries between topologically distinct phases and analyze how finite system sizes influence quantum walk dynamics. For finite lattices, we show that topology induces localized and bilocalized states, leading to Rabi-like transport as a result of degeneracy breaking due to finite-size effects. The study bridges the gap between topological protection and size-dependent dynamics, revealing transitions from ballistic motion to localized or oscillatory behavior based on the system’s topological properties. Analytical and numerical methods are employed to explore the spectra and dynamics of quantum walks, highlighting the robustness of Rabi transport against disorder. The findings provide insights into controlled quantum transport and potential applications in quantum information processing.Abstract This paper investigates Rabi transport and finite-size effects in one-dimensional discrete-time topological quantum walks. We demonstrate the emergence of localized states at boundaries between topologically distinct phases and analyze how finite system sizes influence quantum walk dynamics. For finite lattices, we show that topology induces localized and bilocalized states, leading to Rabi-like transport as a result of degeneracy breaking due to finite-size effects. The study bridges the gap between topological protection and size-dependent dynamics, revealing transitions from ballistic motion to localized or oscillatory behavior based on the system’s topological properties. Analytical and numerical methods are employed to explore the spectra and dynamics of quantum walks, highlighting the robustness of Rabi transport against disorder. The findings provide insights into controlled quantum transport and potential applications in quantum information processing.

arXiv:2506.19523New Journal of PhysicsFeb 1, 20260 citations

Finite-size and interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations

Hsiang-Hsuan Hung, Victor Chua, Lei Wang +1 more

We theoretically study topological phase transitions in two generalized versions of the Kane-Mele-Hubbard model on a finite portion of the honeycomb lattice with up to $2\times 18^2$ sites. Both models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo calculations to be performed in the low-temperature regime. We numerically compute the $Z_2$ invariant and the spin-Chern number directly from the zero-frequency single-particle Greens function for different values of on-site interaction and tune tight-binding parameters to drive topological phase transitions. While phase boundaries are nearly identical for different system sizes, we find a rather strong system-size dependence of the spin Chern number, with the expected quantized value only slowly approached for the largest system sizes. Moreover, we find that quantum fluctuation effects from interactions can act both to stabilize and destabilize topological phases, depending on the details of the model.We theoretically study topological phase transitions in two generalized versions of the Kane-Mele-Hubbard model on a finite portion of the honeycomb lattice with up to $2\times 18^2$ sites. Both models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo calculations to be performed in the low-temperature regime. We numerically compute the $Z_2$ invariant and the spin-Chern number directly from the zero-frequency single-particle Greens function for different values of on-site interaction and tune tight-binding parameters to drive topological phase transitions. While phase boundaries are nearly identical for different system sizes, we find a rather strong system-size dependence of the spin Chern number, with the expected quantized value only slowly approached for the largest system sizes. Moreover, we find that quantum fluctuation effects from interactions can act both to stabilize and destabilize topological phases, depending on the details of the model.

Jul 10, 20131 citation

Theory of finite-size scaling in dynamical quantum phase transitions

Gui-Zhong Yao, Liang-You Peng, Qihuang Gong

Physical Review ASep 2, 20252 citations

We theoretically study topological phase transitions in two generalized versions of the Kane-Mele-Hubbard model on a finite portion of the honeycomb lattice with up to

2\times 18^2

sites. Both models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo calculations to be performed in the low-temperature regime. We numerically compute the

Z_2

invariant and the spin-Chern number directly from the zero-frequency single-particle Greens function for different values of on-site interaction and tune tight-binding parameters to drive topological phase transitions. While phase boundaries are nearly identical for different system sizes, we find a rather strong system-size dependence of the spin Chern number, with the expected quantized value only slowly approached for the largest system sizes. Moreover, we find that quantum fluctuation effects from interactions can act both to stabilize and destabilize topological phases, depending on the details of the model.