{
  "id": "2102.08381",
  "version": "v1",
  "published": "2021-02-16T19:00:00.000Z",
  "updated": "2021-02-16T19:00:00.000Z",
  "title": "Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions",
  "authors": [
    "M. Buchhold",
    "Y. Minoguchi",
    "A. Altland",
    "S. Diehl"
  ],
  "comment": "18+7 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cond-mat.quant-gas",
    "quant-ph"
  ],
  "abstract": "A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. To access it despite the randomness of single quantum trajectories, we construct an $n$-replica Keldysh field theory for the ensemble average of the $n$-th moment of the trajectory projector. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely, while $n-1$ others can be cast into the form of pure state evolutions generated by an effective non-Hermitian Hamiltonian. This decoupling is exact for free theories, and useful for interacting ones. In particular, we study locally measured Dirac fermions in $(1+1)$ dimensions, which can be bosonized to a monitored interacting Luttinger liquid at long wavelengths. For this model, the non-Hermitian Hamiltonian corresponds to a quantum Sine-Gordon model with complex coefficients. A renormalization group analysis reveals a gapless critical phase with logarithmic entanglement entropy growth, and a gapped area law phase, separated by a Berezinskii-Kosterlitz-Thouless transition. The physical picture emerging here is a pinning of the trajectory wave function into eigenstates of the measurement operators upon increasing the monitoring rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-16T19:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "measurement-induced phase transition",
      "effective theory",
      "locally measured dirac fermions",
      "measurements undergoes pure state dynamics",
      "probabilistic measurement induced state updates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}