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Nonequilibrium topological response under charge dephasing

Shuangyuan Lu, Lucas Q Silveira, Yizhi You

Abstract

We explore nonequilibrium topological responses of symmetry-protected topological (SPT) states in open quantum systems subject to decoherence. For SPT wavefunctions protected by a product symmetry G $\times$ S , where G defects are decorated with S charge, we show that local dephasing of the S charge density generically induces spontaneous strong-to-weak symmetry breaking (SWSSB) of G in the resulting mixed-state ensemble. We extend this mechanism to SPT phases protected by higher-form and spatially modulated symmetries, and further to gapless SPT states, demonstrating that dephasing-induced SWSSB persists well beyond conventional gapped 0-form settings. Our results provide a qualitative, channel-defined fingerprint of SPT order that is intrinsic to open-system dynamics and goes beyond equilibrium linear response.

Nonequilibrium topological response under charge dephasing

Abstract

We explore nonequilibrium topological responses of symmetry-protected topological (SPT) states in open quantum systems subject to decoherence. For SPT wavefunctions protected by a product symmetry G S , where G defects are decorated with S charge, we show that local dephasing of the S charge density generically induces spontaneous strong-to-weak symmetry breaking (SWSSB) of G in the resulting mixed-state ensemble. We extend this mechanism to SPT phases protected by higher-form and spatially modulated symmetries, and further to gapless SPT states, demonstrating that dephasing-induced SWSSB persists well beyond conventional gapped 0-form settings. Our results provide a qualitative, channel-defined fingerprint of SPT order that is intrinsic to open-system dynamics and goes beyond equilibrium linear response.
Paper Structure (27 sections, 1 theorem, 148 equations, 8 figures)

This paper contains 27 sections, 1 theorem, 148 equations, 8 figures.

Table of Contents

  1. Motivation
  2. Decoherence-induced SWSSB
  3. Dephasing the SPT Wavefunction
  4. ZXZ Cluster Model
  5. Conditional Mutual Information and Entanglement Negativity
  6. Physical Interpretation
  7. Decohere the 1d Haldane chain
  8. Charge dephasing of Quantum Spin Hall State
  9. charge dephasing in higher-form SPT
  10. Intrinsically Gapless SPT
  11. General Discussion and Outlook
  12. 1d SPT with Symmetry Group $G \times S$
  13. MPS Argument
  14. Discussion for Modulated SPT States
  15. Discussion and Outlook for Generic SPT States in Higher Dimensions
  16. ...and 12 more sections

Key Result

Proposition 1

For an SPT wavefunction protected by a $G\times S$ symmetry, where $G$-defects are decorated by $S$ charge, applying a decoherence channel that measures (or dephases) the local $S$-charge density generically drives strong-to-weak spontaneous symmetry breaking (SWSSB) of the $G$ symmetry in the resul

Figures (8)

  • Figure 1: String order parameter $O_{\text{str}}(r, r^\prime)$ (blue) for ZXZ model ground state $|\psi (h)\rangle$ and Rényi-2 correlator $R^{(2)}(r, r^\prime)$ (orange) for the decohered mixed state $\rho(h)$\ref{['eq.zxz_mixed_state']} versus magnetic field strength $h$ . DMRG parameters: Open boundary condition, system size $L = 1000$, bond dimension $\chi=100$, up to 100 sweeps. $2r = L / 4, 2r^\prime = 3L/4$.
  • Figure 2: Strange correlator (blue) for ZXZ model ground state $|\psi(h)\rangle$ and type-II strange correlator for decohered state $\rho(h)$\ref{['eq.zxz_mixed_state']} versus field strength $h$. DMRG parameters: Open boundary condition, system size $L = 1000$, bond dimension $\chi=100$, up to 100 sweeps. $2r = L / 4, 2r^\prime = 3L/4$.
  • Figure 3: (a) CMI $I(A:B|C)$ and (b) Negativity $\mathcal{N}(\rho)$ for the decohered mixed state $\rho(h)$\ref{['eq.zxz_mixed_state']} versus field strength $h$. DMRG parameters: system size $L = 1000$, bond dimension $\chi=100$, up to 100 sweeps.
  • Figure 4: String order parameter (blue) for the ground state $|\psi(D)\rangle$ of the spin-1 model \ref{['eq.spin_1_hamiltonian']} and Rényi-2 correlator (orange) for the decohered mixed state $\rho(D)$ in \ref{['eq.spin_1_mixed_state']}. DMRG parameters: Open boundary condition, system size $L = 4000$, bond dimension $\chi=100$, up to 100 sweeps. $r = L / 4, r^\prime = 3L/4$.
  • Figure 5: (a) Rényi-2 correlator \ref{['eq.renyi_2_qshe_S']} versus distance $r$. Periodic boundary condition is used, therefore $r=20$ is equivalent to $r=0$. (b) Logarithm $\ln { R^{(2)}}$ versus logarithm of distance $\ln r$. This linearity indicates that the correlation has power-law decay. Monte Carlo simulation parameters: $L = 20$, update $200$k steps, measure for each $10$ steps. Decoherence strength $p=\frac{1}{2}$, Haldane model parameters: $t_1 = 1, t_2 = 0.3, m=0, \phi=\pi/2$.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Proposition 1