Hydrodynamics in lattice models with continuous non-Abelian symmetries

Glorioso, Paolo; Delacrétaz, Luca V.; Chen, Xiao; Nandkishore, Rahul; Lucas, Andrew

doi:10.21468/scipostphys.10.1.015

Cited by 56 publications

(70 citation statements)

References 76 publications

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“…This is despite the fact that the heuristic linear-response argument requires this, or otherwise involves the Kubo-Mori-Bogoliubov inner product [40,87] (but we expect the same results to hold using this inner product). The question of how non-abelian charges affect hydrodynamics has been discussed in the literature, see the recent viewpoints given in [88,89], and in particular their connection with super-diffusion [90].…”

Section: The Problem Of Finite-dimensionality Is Nontrivial In Non-integrable Models Perhapsmentioning

confidence: 99%

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

Doyon

2022

Commun. Math. Phys.

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One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space and time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the $$C^*$$ C ∗ algebra description of statistical mechanics by the Gelfand–Naimark–Segal construction. Using Araki’s exponential clustering and the Lieb–Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states.

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Section: The Problem Of Finite-dimensionality Is Nontrivial In Non-integrable Models Perhapsmentioning

confidence: 99%

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

Doyon

2022

Commun. Math. Phys.

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“…Even more generally, it is typically the case that even if local operators fail to commute, the operators will commute in the thermodynamic limit. A transparent example of this can be found in the hydrodynamics of a system with a non-Abelian flavor symmetry [57]: even though the charge density operators do not commute, in the thermodynamic limit this commutator becomes very small; as a consequence, there are hydrodynamic modes for all flavor charges. Henceforth, from here on out, we will assume (3.2) when building our ideal hydrodynamic action.…”

Section: Factorizabilitymentioning

confidence: 99%

Hydrodynamic effective field theories with discrete rotational symmetry

Huang,

Lucas

2022

Preprint

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We develop a hydrodynamic effective field theory on the Schwinger-Keldysh contour for fluids with charge, energy, and momentum conservation, but only discrete rotational symmetry. The consequences of anisotropy on thermodynamics and first-order dissipative hydrodynamics are detailed in some simple examples in two spatial dimensions, but our construction extends to any spatial dimension and any rotation group (discrete or continuous). We find many possible terms in the equations of motion which are compatible with the existence of an entropy current, but not with the ability to couple the fluid to background gauge fields and vielbein.

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“…Before turning to our main topic of estimating backflow corrections, it is worth first clarifying how correlation functions behave in the absence of truncation, in the longtime regime where hydrodynamics holds sway [19]. While these results are well known, we are not aware of any reference that presents all the facts that we require for our analysis, so we will need to synthesize results from multiple works [19][20][21][22][23][24] into a unified picture.…”

Section: Setting and Conventionsmentioning

confidence: 99%

Operator backflow and the classical simulation of quantum transport

von Keyserlingk,

Pollmann,

Rakovszky

2021

Preprint

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Tensor product states have proved extremely powerful for simulating the area-law entangled states of many-body systems, such as the ground states of gapped Hamiltonians in one dimension. The applicability of such methods to the dynamics of many-body systems is less clear: the memory required grows exponentially in time in most cases, quickly becoming unmanageable. New methods reduce the memory required by selectively discarding/dissipating parts of the many-body wavefunction which are expected to have little effect on the hydrodynamic observables typically of interest: for example, some methods discard fine-grained correlations associated with n-point functions, with n exceeding some cutoff * . In this work, we present a theory for the sizes of 'backflow corrections', i.e., systematic errors due to discarding this fine-grained information. In particular, we focus on their effect on transport coefficients. Our results suggest that backflow corrections are exponentially suppressed in the size of the cutoff * . Moreover, the backflow errors themselves have a hydrodynamical expansion, which we elucidate. We test our predictions against numerical simulations run on random unitary circuits and ergodic spin-chains. These results lead to the conjecture that transport coefficients in ergodic diffusive systems can be captured to a given precision with an amount of memory scaling as exp î O(log( ) 2 ) ó , significantly better than the naive estimate of memory exp O(poly( −1 )) required by more brute-force methods.

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Hydrodynamics in lattice models with continuous non-Abelian symmetries

Cited by 56 publications

References 76 publications

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

Hydrodynamic effective field theories with discrete rotational symmetry

Operator backflow and the classical simulation of quantum transport

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