arXiv subjects

Tobias Swann

Publications and source records attributed to Tobias Swann.

3 recordsLinked to original sources

arXiv2026

Continuum mechanics of entanglement in noisy interacting fermion chains

We develop an effective continuum description for information scrambling in a chain of randomly interacting Majorana fermions. The approach is based on the semiclassical treatment of the path integral for an effective spin chain that describes "two-replica" observables such as the entanglement purity and the OTOC. This formalism gives exact results for the entanglement membrane and for operator spreading in the limit of weak interactions. In this limit there is a large crossover lengthscale between free and interacting behavior, and this large lengthscale allows for a continuum limit and a controlled saddle-point calculation. The formalism is also somewhat different from that known from random unitary circuits. The entanglement membrane emerges as a kind of bound state of two travelling waves, and shows an interesting unbinding phenomenon as the velocity of the entanglement membrane approaches the butterfly velocity.

cond-mat.stat-mech↗

arXiv2023

Nonlinear sigma models for monitored dynamics of free fermions

We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multi-flavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain, and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal $N\times N$ matrix, in the replica limit $N\to 1$. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases -- nontrivially entangled and disentangled respectively -- in the physically-relevant replica limit $N\to 1$. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size $L$ scales as $(\log L)^2$, in contrast to findings in previously-studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model's phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems.

cond-mat.stat-mech↗

arXiv2023

Spacetime picture for entanglement generation in noisy fermion chains

Studies of random unitary circuits have shown that the calculation of Renyi entropies of entanglement can be mapped to classical statistical mechanics problems in spacetime. In this paper, we develop an analogous spacetime picture of entanglement generation for random free or weakly interacting fermion systems without conservation laws. We first study a free-fermion model, namely a 1D chain of Majorana modes with nearest neighbour hoppings, random in both space and time. We analyze the Nth Renyi entropy of entanglement using a replica formalism, and we show that the effective model is equivalent to an SO(2N) Heisenberg spin chain evolving in imaginary time. By applying a saddle-point approximation to the coherent states path integral for the N = 2 case, we arrive at a semiclassical picture for the dynamics of the entanglement purity, in terms of two classical fields in spacetime. The classical solutions involve a smooth domain wall that interpolates between two values, with this domain wall relaxing diffusively in the time direction. We then study how adding weak interactions to the free-fermion model modifies this spacetime picture, reflecting a crossover from diffusive to ballistic spreading of information.

cond-mat.stat-mech↗