Information Geometry of Quantum Phase Transitions

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TECHNICAL SUMMARY:This award supports theoretical and computational research, and education with an aim to develop a quantum information geometry approach to critical phenomena, and to apply it to correlated many-body systems of high physical relevance. Specifically, the PIs will combine analytical, for example development of quantum distinguishability measures, application to exactly solvable models, and computational techniques, such as Quantum Monte Carlo and strong-disorder renormalization group, to investigate the emergence of topological order in quantum spin systems, analyze the effects of disorder on quantum phase transitions, and study the consequences of environment-induced decoherence on quantum criticality.In contrast to traditional approaches, the proposed information geometry analysis of phase transitions is not based on an a priori identification of order parameters, and hence does not require knowledge of symmetry breaking patterns. Instead, systems are analyzed using fidelity measures which quantify the proximity of two system states with different parameter sets. So, the PIs hope this strategy will enable them to gain physical insight into traditionally hard problems, systems for which the order parameter is either unknown, hidden or not defined.This metric approach shifts the traditional emphasis from Hamiltonians to the analysis of quantum states themselves, or put another way, from studying order parameters to universal geometrical structures underlying the way quantum matter organizes itself into different phases.This award supports an outreach effort that involves a collaboration with local physics teachers who work at underprivileged inner-city high schools in the Los Angeles area. This activity supports a network for participating teachers through annual workshops, training sessions and frequent campus visits.NONTECHNICAL SUMMARY:This award supports theoretical and computational research, and education with an aim to develop a different approach to understanding how one state of matter transforms into another. The way atoms are organized can distinguish different sates of matter, for example atoms arranged on a regular array in crystalline solid verses a random arrangement of atoms in liquid. Recent research suggests that this notion is not complete and there are more subtle distinctions between states of matter. This research combines ideas from the emerging area of quantum information theory and computer simulation methods used to study magnetism and other states of matter in complex materials, to investigate new states of matter that may emerge from strong interactions among electrons that may have more subtle differences that are not distinguished in the standard theory of phase transitions. The research is fundamental but involves the interaction of the emerging area of quantum information science with condensed matter theory. The synergy between these areas may lead to new advances and new directions. The research may also have impact on the fundamental principles that may enable the exploitation of the ability to manipulate quantum mechanical states for computation and communication.Apart from educating the next generation of scientists in advanced theoretical methods, this award supports an outreach effort that involves a collaboration with local physics teachers who work at underprivileged inner-city high schools in the Los Angeles area. This activity supports a network for participating teachers through annual workshops, training sessions and frequent campus visits.