Broken Symmetries

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

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Gauge theory approach to branes and spontaneous symmetry breaking

Reviews in Mathematical Physics ◽

10.1142/s0129055x1750009x ◽

2017 ◽

Vol 29 (03) ◽

pp. 1750009 ◽

Cited By ~ 3

Author(s):

A. A. Zheltukhin

Keyword(s):

Gauge Theory ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Vector Fields ◽

Theory Approach ◽

Tensor Fields ◽

Broken Symmetries ◽

Goldstone Bosons ◽

Dimensional Minkowski Space ◽

Poincaré Symmetry

We discuss the gauge theory approach to consideration of the Nambu–Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries. The approach is generalized to describe the fundamental branes in terms of [Formula: see text]-dimensional worldvolume gauge and massless tensor fields consisting of the Nambu–Goldstone bosons associated with the spontaneously broken Poincaré symmetry of the [Formula: see text]-dimensional Minkowski space.

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Spontaneously Broken Symmetries

10.1093/oso/9780192844200.003.0014 ◽

2021 ◽

pp. 287-303

Author(s):

J. Iliopoulos ◽

T.N. Tomaras

Keyword(s):

Phase Transitions ◽

Vector Field ◽

Quantum Physics ◽

Goldstone Boson ◽

Internal Symmetry ◽

Higgs Mechanism ◽

Broken Symmetry ◽

Massive Vector ◽

Broken Symmetries ◽

Gauge Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

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Symmetry

10.1093/oso/9780192846839.003.0005 ◽

2021 ◽

pp. 52-64

Author(s):

Adrian P Sutton

Keyword(s):

Physical Properties ◽

Equations Of Motion ◽

Topological Defects ◽

Phase Changes ◽

Broken Symmetry ◽

Broken Symmetries ◽

Higher Dimensional ◽

Continuous Symmetries ◽

Dimensional Crystal ◽

Deep Sense

Symmetry arises not only in the invariance of an object to certain operations, but also in invariance of the equations governing motion of particles. Noether’s theorem connects continuous symmetries of equations of motion to conservation laws. The concept of broken symmetry arises in phase changes and topological defects, such as dislocations and disclinations. The principle of symmetry compensation reveals a deep sense in which symmetry is never destroyed – broken symmetries relate variants of an object displaying reduced symmetry. Symmetry plays a fundamental role in characterising the physical properties of crystals through Neumann’s principle. The concept of quasiperiodicity is introduced and it is shown how it is related to periodicity in a higher dimensional crystal.

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Task-Layer Multiplicity as a Measure of Community Level Health

Complexity ◽

10.1155/2019/1082412 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8

Author(s):

P. Fraundorf

Keyword(s):

Belief Systems ◽

Well Being ◽

Community Level ◽

Behavioral Measure ◽

Policy Changes ◽

Web Searches ◽

Individual Level ◽

Broken Symmetries ◽

Attention Focus ◽

The Impact

The insights of many disciplines, and of commonsense, about individual-level well-being might be strengthened by a shift in focus to community-level well-being in a way that respects belief systems as well as the power of each individual. We start with the jargon of complex systems and the possibility that a small number of broken symmetries, marked by the edges of a hierarchical series of physical subsystem types, underlie the delicate correlation-based complexity of life on our planet’s surface. We show that an information-theory-inspired model of attention-focus on correlation layers, which looks in/out from the boundaries of skin, family, and culture, predicts that behaviorally diverse communities may tend toward a characteristic task-layer multiplicity per individual of only e29/20≅ 4.26 of the six correlation layers that comprise that community. This behavioral measure of opportunity may help us to (i) go beyond GDP in quantifying the impact of policy changes and disasters, (ii) manage electronic idea-streams in ways that strengthen community networks, and (iii) leverage our paleolithic shortcomings toward the enhancement of community-level task-layer diversity. Empirical methods for acquiring task-layer multiplicity data are in their infancy, although for human communities a great deal of potential lies in the analysis of web searches and asynchronous experience sampling similar to that used by “flu near you.”

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