Hydrodynamics as the effective field theory of strong-to-weak spontaneous symmetry breaking

Abstract

Inspired by the hunt for new phases of matter in quantum mixed states, it has recently been proposed that the equivalence of microcanonical and canonical ensembles in statistical mechanics is a manifestation of strong-to-weak spontaneous symmetry breaking (SWSSB) in an underlying many-body quantum description. Here, we build an effective field theory for SWSSB of a global U(1) symmetry; the answer exactly reproduces the Schwinger-Keldysh effective field theory of diffusion for the conserved charge. We conclude that hydrodynamics can be understood as a theory of "superfluidity" for the broken strong symmetry: a non-vanishing susceptibility is a measurable order parameter for SWSSB, the diffusion mode is the Goldstone boson of the spontaneously broken continuous symmetry, and a generalization of Goldstone's Theorem implies that the diffusion mode is always long-lived. This perspective provides a transparent physical explanation for the unusual "reparameterization" symmetries which are a necessary ingredient of Schwinger-Keldysh effective field theories for "normal fluids".

added appendix discussing reparametrization symmetry for hydrodynamics of 1+1d Dirac fermion

References in corpus (14)

• Quantum criticality under decoherence or weak measurement
• Average Symmetry-Protected Topological Phases
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
• Symmetry protected topological phases under decoherence
• Separability transitions in topological states induced by local decoherence
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
• Measurement-induced phases of matter require feedback
• Symmetry-enforced many-body separability transitions
• The Schwinger-Keldysh Coset Construction
• Designing open quantum systems with known steady states: Davies generators and beyond
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Hydrodynamic effective field theories with discrete rotational symmetry
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

Cited by in corpus (18)

• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the Rényi-1 Correlator
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Hardness of observing strong-to-weak symmetry breaking
• Mixed-State Topological Order under Coherent Noise
• Many-body quantum catalysts for transforming between phases of matter
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Parent Lindbladians for Matrix Product Density Operators
• Non-equilibrium charge-vortex duality
• Emergent Viscous Hydrodynamics From a Single Quantum Particle
• Dynamics in the presence of local symmetry-breaking impurities
• Effective field theory for dissipative photons from higher-form symmetries
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Holographic duality between bulk topological order and boundary mixed-state order
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity