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Active quantum matter from monitored pure-state dynamics

Jacob F. Steiner, Felix von Oppen, Reinhold Egger

Abstract

Quantum many-body systems coupled to out-of-equilibrium reservoirs can behave as active matter and exhibit signs of flocking. However, the resulting steady states are highly mixed and carry only weak quantum signatures. We show that signatures of active matter also arise in ensembles of pure states undergoing monitored quantum dynamics. We consider a spinful Luttinger liquid subject to measurement processes that shuffle spin-up particles to the left and spin-down particles to the right. For weak monitoring strengths and ferromagnetic spin interactions, we find power-law quantum correlations between spin current and charge density, which we identify as a hallmark of active quantum matter. The monitoring plays a dual role, generating the quantum active correlations for weak strengths while driving a Berezinskii-Kosterlitz-Thouless (BKT) phase transition to a shortrange correlated state at larger strengths.

Active quantum matter from monitored pure-state dynamics

Abstract

Quantum many-body systems coupled to out-of-equilibrium reservoirs can behave as active matter and exhibit signs of flocking. However, the resulting steady states are highly mixed and carry only weak quantum signatures. We show that signatures of active matter also arise in ensembles of pure states undergoing monitored quantum dynamics. We consider a spinful Luttinger liquid subject to measurement processes that shuffle spin-up particles to the left and spin-down particles to the right. For weak monitoring strengths and ferromagnetic spin interactions, we find power-law quantum correlations between spin current and charge density, which we identify as a hallmark of active quantum matter. The monitoring plays a dual role, generating the quantum active correlations for weak strengths while driving a Berezinskii-Kosterlitz-Thouless (BKT) phase transition to a shortrange correlated state at larger strengths.
Paper Structure (9 sections, 66 equations, 2 figures)

This paper contains 9 sections, 66 equations, 2 figures.

Table of Contents

  1. Directed hopping monitoring protocol
  2. Bosonization conventions
  3. Replica master equation
  4. Average over the absolute mode
  5. Derivation of the RG flow equations
  6. Current operator
  7. Correlations at the Gaussian fixed points
  8. Weak-coupling fixed point
  9. Strong-coupling fixed point

Figures (2)

  • Figure 1: Cartoon of kinetic processes in the 1D monitored lattice model defined by Eqs. (\ref{['eq:sse']})-(\ref{['eq:lattice_jump_operators']}). Spin-independent and bidirectional motion is due to hopping with amplitude $t_0$ (blue). Spin-dependent unidirectional motion is induced by monitoring with monitoring strength $\gamma$ (red).
  • Figure 2: (a) Phase diagram in the $g_s$--$\gamma$ plane obtained from the RG equations \ref{['eq:RG_eqs']} with $g_c=1$ and $\tilde{c}=\tilde{s}=1/\sqrt{2}$, see Eq. \ref{['eq:couplings']}. The quasi-long-range quantum active phase (small $\gamma$) and the short-range phase (large $\gamma$) are separated by a BKT transition (black line). In the quantum active phase, color indicates the magnitude of $\Delta_{cs}$. The dashed line is an analytical estimate for the phase boundary (see main text). (b-e) Dependence of the coefficients $\{\Sigma_{c/s}^\pm,\Delta_{cs/sc}\}$ on $\gamma$ and $g_s$, which determine the correlations at the fixed point $\lambda=0$, see Eq. \ref{['eq:correlationsfinal']}, using $g_s=2$ in (b) and (d), and $\gamma/v_F = 0.5$ in (c) and (e).