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A<sc>bstract</sc> We explore a large class of correlation measures called theα−zRényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, theα−zRMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values ofαandz, theα−zRMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute theα−zRMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography. 

The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices1–4. However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe2 (refs. 5–8). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDW eventually disappearing at the superconducting critical field Hc2. To understand the phenomenology of this unusual CDW, we construct a Ginzburg–Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe2. 

The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as periodically driven systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic perspective. For general non-integrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the Sachdev-Ye-Kitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the non-saturation of the second Rényi tripartite mutual information. The roles of particle-hole and U(1) symmetries in the SYK model are milder due to the degeneracies being only two-fold, which we confirm explicitly at both large- and small-N. We reinterpret the operator entanglement in terms of the growth of local operators, connecting our results with the information scrambling described by out-of-time-ordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective. 

Abstract We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large- N limit. Using numerical large- N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large- N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.