| quantum phase transitions | |
|---|---|
| Name | Quantum phase transitions |
| Caption | Schematic phase diagram showing a quantum critical point |
| Field | Condensed matter physics |
| Related | Quantum critical point, Quantum many-body problem |
quantum phase transitions Quantum phase transitions are transitions between distinct zero-temperature phases of matter driven by quantum fluctuations rather than thermal energy. They occur when a non-thermal control parameter (such as pressure, magnetic field, or chemical composition) passes a critical value, altering the ground state of a quantum many-body system. Understanding these transitions connects fundamental Condensed matter physics to technologies like quantum computing and has implications for social equity through material accessibility and responsible deployment.
Quantum phase transitions mark qualitative changes in ground-state order as a system parameter is tuned at zero temperature. The central object of study is the quantum critical point where correlation lengths diverge and scale invariance emerges. They provide a window into the Quantum many-body problem and non-perturbative phenomena, informing theories such as Renormalization group and concepts like entanglement entropy. Historically, insights from work by Philip W. Anderson, Subrahmanyan Chandrasekhar, and later researchers such as John A. Hertz and Subir Sachdev have shaped the field. Studying quantum phase transitions is essential for developing materials for superconductivity and platforms for quantum information science.
Quantum phase transitions can be classified by symmetry, order parameter, and topology. Traditional classifications include symmetry-breaking transitions described by an order parameter in the spirit of Landau theory and continuous (second-order) versus first-order transitions. Distinct classes include: - Symmetry-breaking transitions (e.g., magnetic order to paramagnet) exemplified by the Transverse field Ising model. - Topological quantum phase transitions lacking local order parameters, such as transitions between topological insulator phases and trivial insulators, related to concepts from Topology (mathematics) and exemplified in models like the Kitaev chain. - Quantum phase transitions in itinerant electron systems (e.g., ferromagnetic or antiferromagnetic metals) studied in connection with heavy-fermion compounds like CeCu6 and families such as the cuprate superconductors. - Metal–insulator transitions including the Mott transition and the Anderson localization–driven transitions. These classifications guide experiments at institutions such as CERN spin labs, national laboratories (e.g., Argonne National Laboratory, Oak Ridge National Laboratory), and university groups at Harvard University and Massachusetts Institute of Technology.
Theoretical understanding uses model Hamiltonians and field-theoretic methods. Canonical models include the Transverse field Ising model, Heisenberg model, Hubbard model, and Kondo model. Analytical tools include the Renormalization group, Conformal field theory, and large-N expansions; numerical approaches feature Quantum Monte Carlo methods, DMRG, and tensor network states. The role of entanglement entropy and entanglement spectra has been emphasized as diagnostics of phases and criticality. Seminal works include Sachdev's "Quantum Phase Transitions" and foundational papers by Kenneth G. Wilson and Leo Kadanoff on scaling and critical phenomena. Theories also incorporate dissipation and coupling to baths via models developed by Anthony Leggett and collaborators.
At a quantum critical point dynamic critical exponents couple temporal and spatial scaling, encapsulated by the dynamic exponent z and correlation length exponent ν. Quantum critical regions at finite temperature can control crossovers with non-Fermi-liquid behavior as seen in heavy-fermion materials and some high-temperature superconductors. Universal scaling functions connect to experiments measuring thermodynamic and transport observables, and theoretical constructs like hyperscaling and finite-size scaling apply. Quantum criticality also links to emergent phenomena such as deconfined criticality proposed by T. Senthil and colleagues, and to holographic approaches using the AdS/CFT correspondence popularized by Juan Maldacena to model strongly coupled critical points.
Experimental platforms span solid-state materials, ultracold atomic gases, and engineered quantum devices. Solid-state examples include heavy fermion compounds (e.g., YbRh2Si2), cuprate superconductors, and graphene-based systems exhibiting interaction-driven transitions. Ultracold atoms in optical lattices (experiments by groups at Max Planck Institute of Quantum Optics and MIT), using the Bose–Hubbard model, have realized the superfluid–Mott insulator quantum phase transition with high tunability. Measurement techniques include neutron scattering, angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), transport and specific heat measurements, and quantum gas microscopy. Quantum simulators from companies like IBM Quantum and Google Quantum AI provide engineered qubit systems to probe small-scale quantum critical phenomena. Precise control raises questions about equitable access to instrumentation and benefits across communities.
Quantum phase transitions underpin materials with exotic electrical and thermal properties vital for technologies: unconventional superconductors, topological materials for robust qubits, and correlated electron systems for sensors. Understanding quantum criticality may inform design of low-dissipation electronics and resilient quantum error correction architectures. Societal implications include the potential for disruptive economic shifts if advanced materials remain concentrated among wealthy institutions; equitable science policy and open collaboration (e.g., through arXiv and public research funding) are critical to broaden benefits. Ethical deployment, workforce development, and attention to environmental impacts of material extraction and device fabrication should accompany technological advances rooted in quantum phase transition research.
Category:Condensed matter physics Category:Quantum mechanics