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Register a new userA Rigorous Theory of Prethermalization without Temperature
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Prethermalization refers to the physical phenomenon where a system evolves toward some long-lived non-equilibrium steady state before eventual thermalization sets in. One general scenario where this occurs is in driven systems with dynamics governed by an effective Hamiltonian (in some rotating frame), such that ergodicity of the latter is responsible for the approach to the prethermal state. This begs the question whether it is possible to have a prethermal state not associated to any effective Hamiltonian. Here, we answer this question in the affirmative. We exhibit a natural class of systems in which the prethermal state is defined by emergent, global symmetries, but where the dynamics that takes the system to this state has no additional conservation laws, in particular energy. We explain how novel prethermal phases of matter can nevertheless emerge under such settings, distinct from those previously discussed.
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Periodically driven Floquet quantum systems provide a promising platform to investigate novel physics out of equilibrium. Unfortunately, the drive generically heats up the system to a featureless infinite temperature state. For large driving frequency, the heat absorption rate is predicted to be exponentially small, giving rise to a long-lived prethermal regime which exhibits all the intriguing properties of Floquet systems. Here we experimentally observe Floquet prethermalization using nuclear magnetic resonance techniques. We first show the relaxation of a far-from-equilibrium initial state to a long-lived prethermal state, well described by the time-independent prethermal Hamiltonian. By measuring the autocorrelation of this prethermal Hamiltonian we can further experimentally confirm the predicted exponentially slow heating rate. More strikingly, we find that in the timescale when the effective Hamiltonian picture breaks down, the Floquet system still possesses other quasi-conservation laws. Our results demonstrate that it is possible to realize robust Floquet engineering, thus enabling the experimental observation of non-trivial Floquet phases of matter.
While a clean driven system generically absorbs energy until it reaches `infinite temperature, it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for non-trivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localised cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al., [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.
Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s=1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.
To use quantum systems for technological applications we first need to preserve their coherence for macroscopic timescales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. Here we review the state-of-the-art developments in this field in an informative and pedagogical way. We give the main principles of self-correcting quantum memories and we analyze several milestone examples from the literature of two-, three- and higher-dimensional quantum memories.
The 1D AKLT model is a paradigm of antiferromagnetism, and its ground state exhibits symmetry-protected topological order. On a 2D lattice, the AKLT model has recently gained attention because it too displays symmetry-protected topological order, and its ground state can act as a resource state for measurement-based quantum computation. While the 1D model has been shown to be gapped, it remains an open problem to prove the existence of a spectral gap on the 2D square lattice, which would guarantee the robustness of the resource state. Recently, it has been shown that one can deduce this spectral gap by analyzing the models boundary theory via a tensor network representation of the ground state. In this work, we express the boundary state of the 2D AKLT model in terms of a classical loop model, where loops, vertices, and crossings are each given a weight. We use numerical techniques to sample configurations of loops and subsequently evaluate the boundary state and boundary Hamiltonian on a square lattice. As a result, we evidence a spectral gap in the square lattice AKLT model. In addition, by varying the weights of the loops, vertices, and crossings, we indicate the presence of three distinct phases exhibited by the classical loop model.
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