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1. Dynamics in the presence of local symmetry-breaking impurities

   Li, Yahui; Sala, Pablo; Pollmann, Frank; Moudgalya, Sanjay; Motrunich, Olexei I (May 2025, arXivorg)

   Continuous symmetries lead to universal slow relaxation of correlation functions in quantum many-body systems. In this work, we study how local symmetry-breaking impurities affect the dynamics of these correlation functions using Brownian quantum circuits, which we expect to apply to generic non-integrable systems with the same symmetries. While explicitly breaking the symmetry is generally expected to lead to eventual restoration of full ergodicity, we find that approximately conserved quantities that survive under such circumstances can still induce slow relaxation. This can be understood using a super-Hamiltonian formulation, where low-lying excitations determine the late-time dynamics and exact ground states correspond to conserved quantities. We show that in one dimension, symmetry-breaking impurities modify diffusive and subdiffusive behaviors associated with U(1) and dipole conservation at late-times, e.g., by increasing power-law decay exponents of the decay of autocorrelation functions. This stems from the fact that for these symmetries, impurities are relevant in the renormalization group sense, e.g., bulk impurities effectively disconnect the system, completely modifying both temporal and spatial correlations. On the other hand, for an impurity that disrupts strong Hilbert space fragmentation, the super-Hamiltonian only acquires an exponentially small gap, leading to prethermal plateaus in autocorrelation functions which extend for times that scale exponentially with the distance to the impurity. Overall, our approach systematically characterizes how symmetry-breaking impurities affect relaxation dynamics in symmetric systems. 

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2. Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

   https://doi.org/10.1103/PRXQuantum.5.040330  

   Moudgalya, Sanjay; Motrunich, Olexei I (November 2024, PRX Quantum)

   Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a “super-Hamiltonian.” We demonstrate this for conventional symmetries such as ${\mathbb{Z}}_2$, $U\left(1\right)$, and $SU\left(2\right)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped (gapless) super-Hamiltonians indicating the absence (presence) of slow modes, which happens in the presence of discrete (continuous) symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U\left(1\right)$symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality. Published by the American Physical Society2024 

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3. Condensate decay in a radiation dominated cosmology

   https://doi.org/10.1103/PhysRevD.111.063530  

   Cao, Shuyang; Boyanovsky, Daniel (March 2025, Physical Review D)

   Ray, Rashmi (Ed.)

   We study the decay of a homogeneous condensate of a massive scalar field of mass $m$into massless fields in thermal equilibrium in a radiation dominated cosmology. The model is a for the nonequilibrium dynamics of a misaligned axion condensate decaying into radiation. After consistent field quantization in the cosmological background, we obtain the linearized causal equations of motion for a homogeneous condensate including the finite temperature self-energy corrections up to one loop. The dynamical renormalization group is implemented to obtain the time dependent relaxation rate that describes the decay dynamics of the condensate amplitude from stimulated emission and recombination of massless quanta in the medium. It is explicitly shown that a simple friction term in the equation of motion does not describe correctly the decay of the condensate. During the super-Hubble regime, relevant for ultralight dark matter, the condensate amplitude decays as $e^{-\frac{g^2}{10}{t}^2\ln (1/mt)}$. In the sub-Hubble regime the amplitude decays as $e^{-\gamma (t;T(t\left)\right)/2}$with $T\left(t\right)=T_0/a\left(t\right)$; therefore, the finite temperature contribution to the decay rate vanishes fast during the expansion. A main conclusion is that a phenomenological friction term is inadequate to describe the decay in the super-Hubble regime, and the decay function $\gamma \left(t\right)$is always than that from a local friction term as a consequence of the cosmological expansion. For ultralight dark matter, the timescale, during which transient dynamics is sensitive to cosmological expansion and a local friction term is inadequate, is much longer. A friction term always the timescale of decay in the sub-Hubble case. Published by the American Physical Society2025 

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4. Noise-resilient edge modes on a chain of superconducting qubits

   https://doi.org/10.1126/science.abq5769  

   Mi, X.; Sonner, M.; Niu, M. Y.; Lee, K. W.; Foxen, B.; Acharya, R.; Aleiner, I.; Andersen, T. I.; Arute, F.; Arya, K.; et al (November 2022, Science)

   Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with ${\mathbb{Z}}_2$parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment. 

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5. BPS Algebras in 2D String Theory

   https://doi.org/10.1007/s00023-022-01189-7  

   Harrison, Sarah M.; Paquette, Natalie M.; Persson, Daniel; Volpato, Roberto (May 2022, Annales Henri Poincaré)

   Abstract We discuss a set of heterotic and type II string theory compactifications to$$1+1$$ $1+1$dimensions that are characterized by factorized internal worldsheet CFTs of the form$$V_1\otimes \bar{V}_2$$ $V_1\otimes {\overline{V}}_2$, where$$V_1, V_2$$ $V_1,V_2$are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications. 

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