Entanglement Transitions in Unitary Circuit Games
- URL: http://arxiv.org/abs/2304.12965v2
- Date: Wed, 24 Jan 2024 16:30:46 GMT
- Title: Entanglement Transitions in Unitary Circuit Games
- Authors: Ra\'ul Morral-Yepes, Adam Smith, S. L. Sondhi, Frank Pollmann
- Abstract summary: We consider a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds.
We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate.
- Score: 0.16385815610837165
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Repeated projective measurements in unitary circuits can lead to an
entanglement phase transition as the measurement rate is tuned. In this work,
we consider a different setting in which the projective measurements are
replaced by dynamically chosen unitary gates that minimize the entanglement.
This can be seen as a one-dimensional unitary circuit game in which two players
get to place unitary gates on randomly assigned bonds at different rates: The
"entangler" applies a random local unitary gate with the aim of generating
extensive (volume law) entanglement. The "disentangler," based on limited
knowledge about the state, chooses a unitary gate to reduce the entanglement
entropy on the assigned bond with the goal of limiting to only finite (area
law) entanglement. In order to elucidate the resulting entanglement dynamics,
we consider three different scenarios: (i) a classical discrete height model,
(ii) a Clifford circuit, and (iii) a general $U(4)$ unitary circuit. We find
that both the classical and Clifford circuit models exhibit phase transitions
as a function of the rate that the disentangler places a gate, which have
similar properties that can be understood through a connection to the
stochastic Fredkin chain. In contrast, the "entangler" always wins when using
Haar random unitary gates and we observe extensive, volume law entanglement for
all non-zero rates of entangling.
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