Exotic Quantum Criticalities in Low Dimensions and Systems with Unusual Quantum Many-Body Thermalization

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NON-TECHNICAL SUMMARYThis award supports theoretical research studying exotic collective behaviors involving many quantum particles. At absolute zero temperature, such systems can organize into myriad quantum states of matter---quantum phases---depending on details of interactions between particles. While the most common of such phases and their transformations are well understood, some quantum phase transitions do not fit into conventional paradigms, most notably continuous transitions between phases with mismatched orders as can occur in quantum magnets. Yet another class of phases---so-called gapless spin liquids with emergent itinerant quasiparticles---are proposed to occur in several antiferromagnetic solids that defy ordering even at zero temperature. (Here, "liquid" refers to randomness in the directions of the electrons' magnetism inside a solid.) The PI's group will pursue tractable examples of such unusual quantum phase transitions in one and two dimensions and also questions motivated by recent experiments in candidate spin-liquid materials.A different aspect of collective quantum behavior is evolution in time when a system of many particles is started in a non-equilibrium state with finite energy density above zero temperature. This has come to the fore as experimentalists are engineering systems with many degrees of freedom that behave quantum-mechanically, in part in an effort to develop quantum technologies. A fundamental idea to describe such an evolution is that of dynamical thermalization and the closely related eigenstate thermalization hypothesis, which offers a way of understanding why time flows only in one direction. A notable exception to thermalization---so-called many-body localization---occurs in the presence of a large number of impurities. A challenging question, also of technological interest, is whether thermalization can be completely or at least very strongly suppressed in the absence of impurities. The PI's group will continue work on understanding pre-thermalization phenomena and also on so-called quantum many-body scar states that violate the eigenstate thermalization hypothesis.Projects under this award will initiate graduate students to research at the frontier of quantum many-particle physics and will teach them a variety of analytical and numerical approaches that will prepare them for future careers in quantum physics and quantum engineering areas.TECHNICAL SUMMARYThis award supports theoretical research studying different facets of quantum many-body physics: 1) unconventional quantum phase transitions and critical phases at zero temperature, and 2) unusual thermalization dynamics at non-zero energy density above zero temperature.1) While by now we have good ``fixed-point'' pictures of myriad gapped phases, both conventional and exotic, we do not have as good an understanding of quantum phase transitions in many cases. Among these, so-called ``deconfined quantum critical points'' that lie beyond the Landau paradigm have fascinated researchers for more than fifteen years; however, finding truly controlled instances of such critical points has been controversial. Another challenging open problem is the description of gapless fractionalized phases, which are believed to be critical phases that do not require fine-tuning. The PI's group will search for tractable examples of unconventional quantum critical points in low dimensions and will also pursue projects motivated by recent experiments in candidate gapless spin-liquid materials.2) This award will also pursue research in quantum many-body dynamics and thermalization in closed quantum systems. For many years, the interest in such questions had been primarily theoretical, as they relate to foundations of statistical mechanics and notions of quantum chaos. However, modern experiments in engineered quantum systems such as cold atom arrays, trapped ions, dipolar spin impurities, etc., have already achieved well-isolated systems with many quantum degrees of freedom, and are already finding unexpected phenomena opening new exciting directions in the field. In this context, the PI's group will specifically pursue examples of unusual thermalization in systems without disorder and will explore questions of pre-thermalization and quantum many-body scar states. The PI's group studies concrete systems to address challenging open questions and combines and develops both analytical and numerical tools to achieve this.Projects under this award will initiate graduate students to research at the frontier of condensed-matter physics. The students will learn a variety of analytical and numerical approaches to quantum many-body systems that will prepare them for future careers in quantum physics and quantum engineering areas.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.