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This research establishes a unifying principle for quantum phase transitions by rigorously determining their locations across both first- and second-order scenarios in one-parameter lattice Hamiltonians. By extending analytical techniques previously limited to simple state changes, the study provides improved bounds on critical points that are essential for advancing our understanding of fundamental shifts in quantum materials at low temperatures.

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Researchers Bound Locations of Quantum Phase Transitions

Quantum ZeitgeistSeptember 4, 20263 min read

Until now, determining where quantum phase transitions occur within complex materials has been limited to only first-order changes between states. This work extends those analytical techniques to encompass both first and second-order transitions, providing improved bounds on critical points across general one-parameter lattices. Consequently, all such phase transitions may ultimately represent condensations occurring within the system’s available states.

By rigorously establishing locations of quantum phase transitions (QPTs) within one-parameter lattice Hamiltonians, understanding of these fundamental shifts in physical systems has broadened. The analysis extends previous work and now determines locations for both first and second-order QPTs, using a transverse-field Ising model as an explicit example. A unifying principle regarding quantum phase transitions is established; these…

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