Generalized Landau Paradigm Captures Quantum Phases and Transitions Beyond Existing Frameworks

The behaviour of materials undergoing phase transitions, such as changes between solid, liquid, and gas, has long been understood through the Landau paradigm, yet this framework fails to fully explain many complex systems. Xie Chen from the California Institute of Technology and colleagues now propose a generalized version of this paradigm, extending its reach to encompass a wider range of quantum phases and transitions. This new approach leverages recent advances in understanding generalized symmetry and a process called generalized gauging, offering a systematic way to describe how materials change under varying conditions. By successfully broadening the scope of the Landau paradigm, this work provides a powerful tool for investigating complex materials and unlocking new insights into their behaviour.

Fracton-Enhanced Order Parameter for Quantum Phases

Scientists are proposing a generalized Landau paradigm, built upon the concept of a “fracton-enhanced” order parameter, to address limitations in understanding quantum phases and phase transitions. This new framework incorporates both conventional and unconventional orders, including those arising from topological and symmetry-protected topological phases, offering a more comprehensive description of material behaviour. The approach systematically classifies symmetry-allowed operators to define ordered states, then constructs a theoretical model based on these operators, successfully explaining known quantum phases and predicting previously unknown ones. This expands the scope of the original theory and provides a more accurate description of complex material properties.

Symmetry, Topology and Beyond Landau Physics

This research introduces a novel framework extending the Landau paradigm to encompass a broader range of physical systems, particularly those exhibiting symmetries beyond conventional descriptions. The study employs the SymTFT formalism, separating a system’s kinematic symmetry from its dynamic properties, providing a unique structure for analysing critical theories. This approach bridges established methods for understanding systems in one and two dimensions, utilizing conformal and topological quantum field theory respectively. Scientists harness topological holography to explore ‘beyond Landau’ physics and systematically capture phase transitions, constructing a framework based on the breaking of generalized symmetries.

The team investigates systems with unusual symmetries in lower dimensions, where point-like order parameters simplify theoretical descriptions and identification of distinct states of matter. Leveraging the SymTFT formalism, researchers relate emergent symmetries in stable phases to those at transition points, revealing how these symmetries manifest as fundamental properties. In higher dimensions, where conventional methods struggle, scientists demonstrate that emergent symmetries are evident in the energy spectrum rather than correlation functions, providing a powerful tool for understanding complex phase transitions and uncovering novel symmetry structures.

Symmetry Breaking Explains Complex System Behaviour

Scientists are expanding the foundational Landau paradigm by demonstrating a generalized framework capable of capturing phenomena existing beyond its traditional limitations. This work introduces a method for systematically understanding systems through the breaking of generalized symmetries, often achieved via a process called generalized gauging facilitated by topological holography. The team reveals that complex behaviours arise from subtle symmetry breaking patterns, offering a new lens through which to view their properties and delivering a more complete theoretical foundation for analysing a wide range of physical phenomena. Experiments demonstrate that a system with complex symmetry in one spatial dimension plus time can be understood through a structure exhibiting two-dimensional topological order.

Researchers observed that two structures, differing in internal properties, both correspond to fully symmetry-broken phases when subjected to the generalized gauging procedure. This process allows exotic particles to tunnel between boundaries, confirming the symmetry-breaking mechanism. Measurements confirm that this approach successfully maps distinct boundary conditions onto systems exhibiting spontaneously broken symmetry. Further investigations into three-dimensional systems reveal multiple stable boundary conditions, including smooth and twisted smooth boundaries. Applying the generalized gauging procedure to structures with differing boundaries results in systems both exhibiting spontaneously broken symmetry, with detailed analysis revealing that the condensation of specific excitations occurs in distinct ways, leading to the observed symmetry breaking. This establishes a clear connection between boundary conditions and symmetry breaking, providing a powerful tool for understanding and predicting complex system behaviour.

Higher-Form Symmetries and Topological Phases

Scientists are exploring the intricate relationship between symmetry, topology, and topological phases of matter. Traditional symmetries act on points in space, but higher-form symmetries act on extended objects like loops and surfaces. This research aims to understand how these higher-form symmetries can be spontaneously broken and how this manifests in the behaviour of topological phases, particularly at their boundaries. Topological order is a special kind of order that does not rely on breaking conventional symmetries, characterized by topological properties robust against continuous deformations.

The boundaries of a topological phase are crucial, connecting the topologically ordered bulk to a different phase and deeply connected to the symmetries of the bulk. Gapped boundaries possess a finite energy gap, and different gapped boundaries can arise from different ways of condensing exotic particles called anyons, with their condensation determining the boundary condition. Researchers use a “sandwich” model, consisting of a topological phase between two boundaries, to study these relationships, creating a mapping between different boundary conditions to understand whether this mapping corresponds to a transition between spontaneously broken phases. If two boundaries map to each other, it suggests they are both in a broken phase of the same symmetry.

They apply this framework to the Toric Code and more complex systems like 3D Quantum Electrodynamics, also considering a system with a complex symmetry group of order 128, illustrating the mapping between boundaries in a more intricate setting. This research emphasizes the deep connection between boundary conditions and the symmetries of the bulk topological phase, with the ultimate goal of understanding transitions between different boundary conditions and whether these transitions can be interpreted as transitions between spontaneously broken phases. While there are exceptions and complications to the simple mapping, this work provides a sophisticated framework for understanding topological phases of matter and the role of higher-form symmetries.