Entropic Order Defies Expectations by Creating Order at High Temperatures

A new understanding of how order can emerge at high temperatures is being established by Po-Shen Hsin of King’s College London and Ryohei Kobayashi of University of Tokyo. Entropic order can arise even at elevated temperatures, challenging the conventional view that high temperatures invariably lead to disorder and potentially offering new avenues for exploring topological states of matter. The research introduces a new set of tools for building quantum lattice models exhibiting this behaviour, revealing continuous symmetry breaking and chiral topological superconductivity with temperature-independent properties. These models display unique higher-form symmetries and spontaneous symmetry breaking, distinguishing them from conventional topological orders and broadening the scope of possibilities for high-temperature quantum phenomena. Engineering entropic order via bosonic coupling and local Hamiltonians Coupling a low-temperature ordered phase to bosons proved key to unlocking these high-temperature states. This technique adds a new level of interaction to an existing quantum system, attaching it to a collection of bosons, particles that act as force carriers, already in an ordered state. The underlying principle relies on the fact that bosons, due to their quantum mechanical nature, can occupy the same quantum state, leading to collective behaviour and enhanced correlations. By coupling the system to these pre-ordered bosons, the overall entropy of the combined system can be increased while simultaneously maintaining or even enhancing order within the original quantum system. Consequently, the creation of states with higher entropy than disorder becomes possible, defying the usual expectation that heat randomises systems; it’s akin to reinforcing a structure with additional, pre-organised supports. This is particularly significant as it suggests a pathway to circumvent the second law of thermodynamics in specific, carefully engineered scenarios, not by violating it, but by strategically manipulating entropy through these couplings. The strength of this coupling, and the specific properties of the bosons, are crucial parameters in determining the stability and characteristics of the resulting entropic order. For models lacking initial order, a second construction method proved effective, utilising local commuting-projector Hamiltonians, which define the system’s energy based on local interactions. These Hamiltonians, constructed from operators that commute with each other, ensure that the system’s dynamics are governed by interactions confined to a limited spatial region. This locality is essential for maintaining stability and preventing long-range fluctuations that could disrupt the emergent order. These Hamiltonians were coupled to more general bosonic degrees of freedom, offering a general mechanism to explore a wider range of entropic orders in both classical and quantum systems. This approach circumvents the limitations of previous methods, allowing exploration of quantum lattice models exhibiting this phenomenon, where order persists at high temperatures despite expectations of disorder. The commuting-projector construction allows for a systematic way to build Hamiltonians that favour specific ordered states, even in the presence of thermal fluctuations, by effectively projecting out disordered configurations. This is achieved by designing the projectors to select states that satisfy certain local constraints, thereby suppressing the growth of entropy. High-temperature topological superconductivity via entropic order and analytical modelling Chiral topological superconducting states sustained at high temperatures have been demonstrated, achieving temperature-independent anyon correlation functions, a feat previously considered impossible. Anyons are exotic quasiparticles that exhibit fractional statistics, meaning their exchange statistics differ from both bosons and fermions. Their correlation functions describe the probability of finding two anyons at a given distance, and temperature independence implies that these correlations are robust against thermal fluctuations. This breakthrough circumvents the limitations of the Hohenberg-Mermin-Wagner theorems, which typically preclude continuous symmetry breaking in low-dimensional systems. These theorems state that continuous symmetries cannot be spontaneously broken at finite temperatures in systems with dimensions less than or equal to 2, due to the destabilising effect of thermal fluctuations. However, the entropic order mechanism effectively shields the symmetry-breaking field from these fluctuations, allowing for persistent order even at high temperatures. Conventional models fail to maintain order at elevated temperatures, but these new quantum lattice models exhibit persistent order due to coupling to bosons. These models demonstrate spontaneously broken continuous symmetry, even when conventional theories like the Hohenberg-Mermin-Wagner theorems predict disorder; specifically, the models exhibit ferromagnetism at arbitrarily high temperatures. This is a remarkable result, as it implies that the system can maintain a net magnetisation even in the absence of an external magnetic field, and that this magnetisation is not diminished by increasing the temperature. Furthermore, a broad family of high-temperature entropic non-chiral topological orders was revealed, possessing strong higher-form symmetries not found in conventional topological systems. Higher-form symmetries are a generalisation of ordinary symmetries that act on higher-dimensional objects, such as loops or surfaces, rather than on individual particles. These symmetries can lead to the emergence of exotic topological phases with unusual properties. Realising these states in physical materials and controlling the necessary bosonic couplings remains a vital challenge. Identifying materials with appropriate bosonic excitations and engineering the necessary interactions between these bosons and the quantum lattice is a significant hurdle that requires further investigation. Harnessing thermal fluctuations for stable quantum states via entropic order The pursuit of stable quantum states at practical temperatures has long been hampered by the tendency of heat to induce disorder. Maintaining quantum coherence, a prerequisite for many quantum technologies, requires isolating the system from its environment to minimise interactions that cause decoherence. However, these new findings demonstrate that order can, in effect, be actively encouraged by thermal fluctuations, a concept termed ‘entropic order’, and offer analytical tools to build models exhibiting this counterintuitive behaviour. This suggests that thermal fluctuations, traditionally viewed as a source of noise, can be harnessed as a resource for stabilising quantum states. A key limitation remains the lack of detail regarding how these bosons might be physically realised within existing materials. Acknowledging that realising the necessary bosonic components within existing materials presents a hurdle, this work nonetheless establishes a theoretical framework. It demonstrates that order isn’t always diminished by heat; instead, arrangements involving bosons can use thermal energy to create stable, topologically interesting quantum states. This challenges conventional understanding and opens avenues for designing novel materials with predictable properties at high temperatures, potentially impacting areas like superconductivity and quantum field theories. The ability to engineer materials that exhibit stable quantum behaviour at elevated temperatures could revolutionise various fields, including energy storage, quantum computing, and materials science. This challenges conventional understanding and opens avenues for designing novel materials with predictable properties at high temperatures, potentially impacting areas like superconductivity and quantum field theories. The discovery of ‘entropic order’ challenges the established link between temperature and disorder in quantum systems; conventional wisdom suggests heat randomises arrangements, yet these findings demonstrate specific quantum lattice models can maintain, and even enhance, order at high temperatures. New analytical methods constructing models that utilise local Hamiltonians with broader bosonic interactions achieved this. These constructions circumvent limitations like the Hohenberg-Mermin-Wagner theorems, which typically preclude continuous symmetry breaking at finite temperatures, and reveal strong higher-form symmetries not seen in conventional topological systems. The development of these analytical tools provides a powerful framework for exploring new quantum phenomena and designing materials with tailored properties, paving the way for future advancements in quantum technologies and fundamental physics. The research demonstrated that order can be maintained, and even enhanced, in specific quantum lattice models at high temperatures, a phenomenon termed ‘entropic order’. This finding challenges the conventional expectation that increased temperature leads to greater disorder within a system. Researchers developed new analytical methods to construct these models, utilising local Hamiltonians and bosonic interactions to achieve stable, topologically interesting quantum states. These models exhibit strong higher-form symmetries and circumvent established theorems limiting symmetry breaking at high temperatures, offering a new framework for exploring quantum phenomena. 👉 More information🗞 Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models🧠 ArXiv: https://arxiv.org/abs/2604.18694 Tags: