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Exact Quench Dynamics from Thermal Pure Quantum States

Hui-Huang Chen

Abstract

We present an exact solution for the real-time dynamics following a quench from a thermal pure quantum (TPQ) state in an integrable system. Although equilibration is expected in this setting because the TPQ state already encodes the thermal expectation values of all conserved quantities, the approach to equilibrium shows highly nontrivial coherent dynamics. In the spin-1/2 XX chain, local observables become stationary at their thermal values after dephasing, while the entanglement entropy exhibits a characteristic double-plateau structure. We obtain this behavior exactly using three complementary approaches: two-dimensional (2D) conformal field theory (CFT) on the Klein bottle, an exact numerical evolution based on the matrix Riccati equation, and an asymptotically exact quasiparticle picture. These results demonstrate that the non-monotonic entanglement evolution is a macroscopic manifestation of the coherent dephasing of anomalous pairing correlations in the initial TPQ state.

Exact Quench Dynamics from Thermal Pure Quantum States

Abstract

We present an exact solution for the real-time dynamics following a quench from a thermal pure quantum (TPQ) state in an integrable system. Although equilibration is expected in this setting because the TPQ state already encodes the thermal expectation values of all conserved quantities, the approach to equilibrium shows highly nontrivial coherent dynamics. In the spin-1/2 XX chain, local observables become stationary at their thermal values after dephasing, while the entanglement entropy exhibits a characteristic double-plateau structure. We obtain this behavior exactly using three complementary approaches: two-dimensional (2D) conformal field theory (CFT) on the Klein bottle, an exact numerical evolution based on the matrix Riccati equation, and an asymptotically exact quasiparticle picture. These results demonstrate that the non-monotonic entanglement evolution is a macroscopic manifestation of the coherent dephasing of anomalous pairing correlations in the initial TPQ state.

Paper Structure

This paper contains 17 sections, 162 equations, 2 figures.

Table of Contents

  1. The CFT approach to the quench dynamics from TPQ states
  2. Crosscap state in free compact boson CFT
  3. The two-point functions
  4. The entanglement entropy
  5. Proof of the identity \ref{['identity']}
  6. Integrating over $\alpha$
  7. Integrating over $\beta$
  8. Imaginary-time v.s. real-time evolution of the fermionic covariance matrix
  9. The imaginary-time evolution
  10. The real-time evolution
  11. The solution of general matrix Riccati equations
  12. Properties of the crosscap states and TPQ states
  13. The pair structure in the thermodynamic limit
  14. The parent Hamiltonian of the crosscap states
  15. The BCS representation of the crosscap state
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Comparison between the exact numerical results and the CFT prediction for the entanglement entropy $S_A(t)$. Solid lines: numerical data; circles: CFT prediction. Left: $L=500, l=80, \beta =20, v_F=1$. Right: $L=400,l=100,\beta=40, v_F=1$.
  • Figure 2: Comparison between the exact numerical results and the quasiparticle prediction for the entanglement entropy $S_A(t)$. Solid lines: numerical data; dashed line: quasi-particle prediction. Left: $L=600, l=200, \beta=1, J=0.5$. Right: $L=1000,l=400,\beta=4,J=0.5$.