University of Science and Technology of: Kpz Dynamics, Not Symmetry Breaking, Govern Open Quantum Systems

Guo-Qiang Wang and colleagues at University of Science and Technology show that Kardar-Parisi-Zhang (KPZ) dynamics, not diffusion predicted by existing spontaneous symmetry breaking (SSB) models, govern the behaviour of an open integrable system, specifically the B3 model. The work details the conditions under which the SSB ansatz fails to accurately describe emergent hydrodynamics, revealing that the B3 model is equivalent to interacting asymmetric XXZ spin chains and exhibits KPZ scaling even with negative hopping rates. These findings advance the theoretical understanding of charge transport in open quantum systems and move beyond current SSB-based approaches.

Choi isomorphism reveals interacting spin chain dynamics in the B3 model

The Choi isomorphism simplified the complex dynamics of the B3 model, recasting it into a more manageable form. This mathematical transformation, a complete positive trace-preserving map, maps operators describing quantum system changes into vectors within a doubled Hilbert space. This effectively represents the system as two interacting spin chains, allowing for a more tractable analysis of its behaviour. The utility of the Choi isomorphism lies in its ability to transform a complex many-body problem into a seemingly simpler, albeit higher-dimensional, equivalent problem, facilitating the application of established techniques from spin chain physics. Consequently, the team focused on disentangling the individual evolution of each chain from the interactions between them, revealing that the B3 model’s behaviour arises from these two components. Understanding the interplay between these chains is crucial for accurately modelling the system’s dynamics.

The B3 model, an open quantum system characterised by its non-equilibrium dynamics, underwent investigation using the Choi isomorphism to simplify its complex behaviour. This recast the system as two interacting spin chains, enabling a focus on disentangling their individual evolution and the interactions between them. The B3 model is particularly interesting as it represents a paradigmatic example of an open system, constantly exchanging energy and information with its environment. Simulations, performed on a chain of 256 spins with a dissipation rate of 1.2 and a bond dimension of 64, moved beyond approximations reliant on spontaneous symmetry breaking, revealing Kardar-Parisi-Zhang dynamics instead of expected diffusive behaviour. The choice of a bond dimension of 64 represents a balance between computational cost and accuracy, ensuring sufficient representation of the quantum state while remaining feasible for numerical simulation. These simulations employed time-evolving block decimation (TEBD), a powerful numerical method for studying the dynamics of quantum many-body systems.

B3 model dynamics transition to Kardar-Parisi-Zhang universality via interacting spin chains

A charge decay rate of 0.426 was observed, significantly faster than previously predicted diffusive transport and fitting instead to a KPZ scaling with a dynamical exponent of 3/2. This represents a substantial improvement over existing models which failed to capture this behaviour. The KPZ universality class describes systems exhibiting anomalous scaling behaviour, characterised by a dynamical exponent of 3/2, and is typically observed in systems far from equilibrium. The finding establishes a threshold where approaches reliant on spontaneous symmetry breaking break down, revealing that the B3 model’s dynamics are governed by Kardar-Parisi-Zhang (KPZ) dynamics even with negative hopping rates, something impossible to predict using earlier methods. Negative hopping rates introduce complexities not typically encountered in standard quantum systems, highlighting the B3 model’s unique characteristics. Analysis revealed the B3 model functions as two interacting asymmetric XXZ spin chains, with the spontaneous symmetry breaking ansatz only accounting for interactions between these chains, not within them. The XXZ spin chain is a fundamental model in quantum magnetism, and its asymmetric variant introduces directional biases in the interactions. Numerical calculations, utilising a time-evolving block decimation method with a chain length of 256 and bond dimension of 64, revealed a charge decay rate fitting a KPZ scaling with a dynamical exponent of 3/2 when observations began around time step 5. This indicates that the interactions within each chain are dominant in determining the short-time dynamics. The data was fitted to a scaling function, achieving parameters of approximately 0.426, and analysing the components of the charge correction function confirmed this; the two-chain component decayed faster, becoming negligible at longer times. Further analysis of the Liouvillian’s spectral gap, and subsequent derivation of an asymmetric XXZ model, demonstrated a scaling of N−3/2, contrasting with the N−2 scaling predicted by the spontaneous symmetry breaking ansatz. The Liouvillian describes the time evolution of the density matrix, and its spectral gap provides information about the system’s relaxation rate.

Charge transport deviates from symmetry breaking in strongly interacting quantum systems

Scientists have long sought a universal description of how energy and information flow in complex quantum systems, with spontaneous symmetry breaking offering a promising, unifying framework. This approach relies on identifying conserved quantities and symmetries to simplify the description of many-body dynamics. However, work with the B3 model reveals a key limitation; this standard approach, while effective in many scenarios, fails to fully capture the dynamics when interactions between components become dominant. Consequently, charge transport instead follows Kardar-Parisi-Zhang (KPZ) dynamics, a more intricate pattern typically observed in growing rough surfaces, challenging the assumed universality of simpler models. The emergence of KPZ dynamics suggests that the system is driven by non-linear effects and fluctuations, which are not adequately captured by linearised theories based on symmetry breaking.

Accurately modelling complex quantum behaviours and refining predictions about energy and information flow requires understanding when and why this standard model breaks down. Work with the B3 model establishes that charge transport can deviate from predictions based on spontaneous symmetry breaking, a commonly used framework for understanding open quantum systems. Dynamics aligning with Kardar-Parisi-Zhang (KPZ) scaling were observed, a pattern more typically associated with the growth of rough surfaces, suggesting the initial theoretical approach inadequately accounts for interactions within the system. The connection to KPZ dynamics opens up new avenues for understanding charge transport in terms of concepts from statistical physics and non-equilibrium dynamics. Demonstrating the B3 model functions as two interacting asymmetric XXZ spin chains clarifies that the spontaneous symmetry breaking ansatz only captures interactions between these chains, overlooking important internal dynamics. This highlights the importance of considering both inter-chain and intra-chain interactions for a complete description of the system’s behaviour. The implications of this research extend to the design of novel quantum devices and materials where understanding and controlling charge transport is paramount.

The research demonstrated that charge transport in the B3 model follows Kardar-Parisi-Zhang (KPZ) dynamics, rather than the diffusion predicted by spontaneous symmetry breaking. This finding matters because it indicates that a commonly used theoretical approach for modelling open quantum systems has limitations when interactions between components are strong. Specifically, the B3 model behaves like two interacting asymmetric XXZ spin chains, and the initial ansatz only accounts for interactions between these chains. This work motivates a revised theory of charge transport in open systems, moving beyond approaches solely based on spontaneous symmetry breaking.