Freezing and Shielding under Global Quenches for Long-Range Interacting Many-Body Systems

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Freezing and Shielding under Global Quenches for Long-Range Interacting Many-Body Systems".

Mira: Here's the gist of the paper. Shielding and freezing are universal features of long-range interacting systems, occurring when local interactions are turned on suddenly in a Fermi-Hubbard model with long-range hopping, leading to the suppression of dynamical signatures from low-energy states The Model and Setup The study investigates the time evolution of a Fermi-Hubbard model with long range hopping following a sudden quench of the local interactions among different spin species.

Kai: The system is described by the Hamiltonian H = H0 + Hint, where H0 involves long-range hopping amplitudes that decay as a power-law of the distance.

Mira: The hopping amplitude tr fluctuates around a mean-value that decays as a power-law of the distance, with the probability distribution of each tr being an independent Gaussian distribution with finite mean and variance.

Kai: The model is analyzed in one dimension (d=1) for correlated electrons to study the dynamics.

Title and authors: Kai: Now they move on to how this freezing changes when you introduce Gaussian disorder into the long range hopping amplitudes. The paper focuses on a specific analytical connection here, linking that accumulation point to a semi-circular density of states in Gaussian random matrices.

Mira: That part about the continuous spectrum appearing due to disorder is key because it unfreezes the dynamics in some way, but they argue that shielding still happens because the long range couplings are confined to just a few low energy discrete states.

Lev: So if we were trying to run this on real hardware with error correction, it suggests that even with some noise, the long range structure doesn't immediately destroy everything; it just gets relegated to those very low energy states.

Kai: It’s like those signatures of the long range hopping are mostly hidden from the main dynamics because they only affect a tiny part of the spectrum.

Mira: And they show that this effect of shielding is what makes these phenomena, freezing and shielding, a universal feature across different power-law exponents, specifically when alpha is less than one.

Lev: So for practical terms, it means that if you're dealing with long range hopping in a material, the global dynamics might look almost exactly like a system without those long range interactions.

The paper's summary: Kai: They summarize their work by focusing on the dynamical mean-field theory or DMFT perspective, showing that as you turn on local interactions at time t greater than zero, a finite potential energy is imprinted but it can't be dispersed in any way.

Mira: And they say this happens universally for any power-law exponent alpha less than one in the thermodynamic limit, which really ties the freezing phenomenon to the structure of the spectrum.

Lev: From an engineering standpoint, if you try to simulate this with DMFT, their self-consistency converges to a simple result in the atomic limit where G minus ten of i omega n equals i omega n plus mu plus O of one over N <ref:2407.06072#pg3>.

Kai: That implies that the dynamics are determined by energies near the Fermi surface, which mirrors what you’d expect from a local system on an infinite dimensional Bethe lattice.

Mira: But they also note that in the presence of disorder, even though there's a continuous semi-circular profile for strong long range interactions when alpha is less than d, there are still discrete spectral features present.

Lev: So the caveat here is that while shielding happens, you still have to account for those specific low energy levels that exist due to the long range structure itself.

The paper's improvements: Kai: The paper suggests a few ways we can use this understanding practically. First, they mention designing adaptive quench response systems where you tune the local interactions specifically so that "the low energy gaps are large enough" to prevent mixing high and low energy modes.

Mira: That would mean actively trying to exploit the freezing mechanism by controlling the local interaction strength precisely at t greater than zero to keep those modes separated.

Lev: If we think about error correction codes, this points toward stabilizing certain states by making sure the local interaction doesn't cause unwanted transitions between subspaces.

Kai: And second, they suggest that long range interacting quantum simulators, like those with Rydberg atom arrays or dipolar systems, could exhibit quasi-stationary states whose lifetimes actually increase with system size because the dynamics are shielded from the long range signatures of the model.

Mira: That would be really useful for experimentalists trying to get long coherence times in these types of setups.

Lev: I see that connecting quasi-stationary states to system size is important, because on real hardware, those large systems might exhibit this shielding effect better than small ones do.

Conclusion: Kai: So wrapping up the paper "Freezing and Shielding under Global Quenches for Long-Range Interacting Many-Body Systems", the main point is that shielding and freezing are universal features in long range interacting systems when local interactions are suddenly turned on.

Mira: The key finding is that in the presence of disorder, shielding becomes clearer because the continuous spectrum forms due to disorder, while long range couplings only affect those few low energy discrete states which become statistically irrelevant in the thermodynamic limit.

Lev: For me, what this means for running real hardware is that we can treat these long range interactions as effectively absent in terms of global dynamics once we're in the large system limit.

Kai: And they link these out-of-equilibrium properties of long range couplings directly to the quasi-particle spectrum, which is observable across various degrees of freedom.

Mira: The final implication is that when you have a large system with Gaussian disorder, the dynamics stabilize as the continuous part of the spectrum equilibrates by dephasing, while those discrete states are shielded by the large system size.

Lev: We're left with this idea that we can look at these systems through a quasi-particle picture and see how it connects to how many-body spectra behave in these complex scenarios.

Kai: That’s what they found in "Freezing and Shielding under Global Quenches for Long-Range Interacting Many-Body Systems". We'll be looking at more of this kind of work next time.