Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0609177 · American Journal of Physics

Spontaneous symmetry breaking in quantum mechanics

Jasper van Wezel, Jeroen van den Brink

Published Jun 12, 2007• 40 citations
arXivHTMLPDF

Abstract

We present a mathematically simple procedure to explain spontaneous symmetry breaking in quantum systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a symmetry broken state in crystals, antiferromagnets, and even superconductors. It has the advantage that it automatically brings to the fore the main players in spontaneous symmetry breaking: the symmetry-breaking field, the thermodynamic limit, and the global excitations of a “thin” spectrum.

DOI
10.1119/1.2730839

Related papers

Quantum dynamics in the thermodynamic limit

Jasper van Wezel

The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum-mechanical building blocks is one of the cornerstones of modern condensed-matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking, however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy---one of the well-known characteristic properties shared by all symmetry-breaking objects---can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum-mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born's rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.

arXiv:0804.3026•Physical Review B•Aug 8, 2008•36 citations

Spontaneous symmetry breaking and decoherence in superconductors

Jasper van Wezel, Jeroen van den Brink

We show that superconductors have a thin spectrum associated with spontaneous symmetry breaking similar to that of antiferromagnets, while still being in full agreement with Elitzur's theorem, which forbids the spontaneous breaking of local (gauge) symmetries. This thin spectrum in the superconductors consists of in-gap states that are associated with the spontaneous breaking of a global phase symmetry. In qubits based on mesoscopic superconducting devices, the presence of the thin spectrum implies a maximum coherence time which is proportional to the number of Cooper pairs in the device. Here we present the detailed calculations leading up to these results and discuss the relation between spontaneous symmetry breaking in superconductors and the Meissner effect, the Anderson-Higgs mechanism, and the Josephson effect. Whereas for the Meissner effect a symmetry breaking of the phase of the superconductor is not required, it is essential for the Josephson effect.

arXiv:0706.1922•Physical Review B•Feb 28, 2008•20 citations

Spontaneous symmetry breaking in quantum frustrated antiferromagnets

P. Azaria, Bertrand Delamotte, D. Mouhanna

We show that the spontaneous symmetry breaking mechanism in quantum antiferromagnets is due to the collapse, in the thermodynamical limit, of an infinite set of excited states onto the ground state. We characterize both the nature and the scaling of the relevant tower of states for the quantum antiferromagnet on the triangular lattice. Comparison with recent numerical results for the S=1/2 case gives strong support for the existence of long range order in this system.

Physical Review Letters•Apr 19, 1993•64 citations

Relation between decoherence and spontaneous symmetry breaking in many-particle qubits

Jasper van Wezel, Jan Zaanen, Jeroen van den Brink

We have recently shown that there is a limit to quantum coherence in many-particle spin qubits due to spontaneous symmetry breaking. These results were derived for the Lieb-Mattis spin model. Here we will show that the underlying mechanism of decoherence in systems with spontaneous symmetry breaking is in fact more general. We present here a generic route to finding the decoherence time associated with spontaneous symmetry breaking in many-particle qubits, and subsequently we apply this approach to two model systems, indicating how the continuous symmetries in these models are spontaneously broken and discussing the relation of this symmetry breaking to the thin spectrum. We then present in detail the calculations that lead to the limit to quantum coherence, which is due to energy shifts in the thin spectrum.

arXiv:cond-mat/0606140•Physical Review B•Sep 27, 2006•38 citations

Spontaneous Symmetry Breaking

Tomáš Brauner

The roots of the modern understanding of symmetries in physics can be traced to the work of Sophus Lie on transformations of differential equations in the nineteenth century. In this chapter, the history of the subject is used to emphasize the distinction between the symmetry of the dynamics of a physical system and the symmetry of its specific state. The central concept of spontaneous symmetry breaking is then introduced as the discrepancy between the two notions of symmetry. It is shown how the presence of spontaneous symmetry breaking can be detected through the sensitivity of measurements on the physical state to external perturbations. This naturally leads to the concepts of the order parameter and the vacuum manifold. The rest of the chapter is devoted to highlighting some subtle features of spontaneous symmetry breaking. These include the properties of the ground state and the tower of low-lying excited states in a finite volume, and the absence of well-defined unitary operators representing broken symmetry in the thermodynamic limit.

Lecture notes in physics•Jan 1, 2024•0 citations

Symmetry Breaking through Superselection by Boundary Conditions

Silvester G. A. Borsboom, José P. Dupont

Spontaneous symmetry breaking (SSB) is central to modern physics but is conventionally defined only for infinite systems, raising challenges for its interpretation in finite, real-world setups. This paper argues that the key to resolving this issue lies in the underappreciated role of boundary conditions in quantum systems. Inspired by both the relational approach to symmetries and the physical mechanism behind symmetry breaking, we formulate a relational interpretation of SSB: a finite system exhibits SSB relative to a reference environment which can induce perturbations across the boundary. This eliminates the need for the thermodynamic limit, offering a more physical picture of SSB that emphasizes the observable consequences of the interactions that real-life systems inevitably have with their environment. We show how, in this relational interpretation, SSB for both lattice systems and (gauge) field theories should be understood as subtle, rather than spontaneous, symmetry breaking, still in contrast to explicit symmetry breaking. We also explain how algebraic definitions of SSB for infinite systems relate to the intuitive picture of SSB in finite systems and illustrate how asymptotic boundary conditions push the environment "to infinity". In this way, our relational interpretation of SSB provides a unified conceptual framework applicable to symmetry-breaking in systems of any size.

physics.hist-phCross-listedarXiv:2606.15272•Jun 16, 2026•0 citations
We present a mathematically simple procedure to explain spontaneous symmetry breaking in quantum systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a symmetry broken state in crystals, antiferromagnets, and even superconductors. It has the advantage that it automatically brings to the fore the main players in spontaneous symmetry breaking: the symmetry-breaking field, the thermodynamic limit, and the global excitations of a “thin” spectrum.
The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum-mechanical building blocks is one of the cornerstones of modern condensed-matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking, however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy---one of the well-known characteristic properties shared by all symmetry-breaking objects---can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum-mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born's rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.
We show that superconductors have a thin spectrum associated with spontaneous symmetry breaking similar to that of antiferromagnets, while still being in full agreement with Elitzur's theorem, which forbids the spontaneous breaking of local (gauge) symmetries. This thin spectrum in the superconductors consists of in-gap states that are associated with the spontaneous breaking of a global phase symmetry. In qubits based on mesoscopic superconducting devices, the presence of the thin spectrum implies a maximum coherence time which is proportional to the number of Cooper pairs in the device. Here we present the detailed calculations leading up to these results and discuss the relation between spontaneous symmetry breaking in superconductors and the Meissner effect, the Anderson-Higgs mechanism, and the Josephson effect. Whereas for the Meissner effect a symmetry breaking of the phase of the superconductor is not required, it is essential for the Josephson effect.
We have recently shown that there is a limit to quantum coherence in many-particle spin qubits due to spontaneous symmetry breaking. These results were derived for the Lieb-Mattis spin model. Here we will show that the underlying mechanism of decoherence in systems with spontaneous symmetry breaking is in fact more general. We present here a generic route to finding the decoherence time associated with spontaneous symmetry breaking in many-particle qubits, and subsequently we apply this approach to two model systems, indicating how the continuous symmetries in these models are spontaneously broken and discussing the relation of this symmetry breaking to the thin spectrum. We then present in detail the calculations that lead to the limit to quantum coherence, which is due to energy shifts in the thin spectrum.
The roots of the modern understanding of symmetries in physics can be traced to the work of Sophus Lie on transformations of differential equations in the nineteenth century. In this chapter, the history of the subject is used to emphasize the distinction between the symmetry of the dynamics of a physical system and the symmetry of its specific state. The central concept of spontaneous symmetry breaking is then introduced as the discrepancy between the two notions of symmetry. It is shown how the presence of spontaneous symmetry breaking can be detected through the sensitivity of measurements on the physical state to external perturbations. This naturally leads to the concepts of the order parameter and the vacuum manifold. The rest of the chapter is devoted to highlighting some subtle features of spontaneous symmetry breaking. These include the properties of the ground state and the tower of low-lying excited states in a finite volume, and the absence of well-defined unitary operators representing broken symmetry in the thermodynamic limit.
Spontaneous symmetry breaking (SSB) is central to modern physics but is conventionally defined only for infinite systems, raising challenges for its interpretation in finite, real-world setups. This paper argues that the key to resolving this issue lies in the underappreciated role of boundary conditions in quantum systems. Inspired by both the relational approach to symmetries and the physical mechanism behind symmetry breaking, we formulate a relational interpretation of SSB: a finite system exhibits SSB relative to a reference environment which can induce perturbations across the boundary. This eliminates the need for the thermodynamic limit, offering a more physical picture of SSB that emphasizes the observable consequences of the interactions that real-life systems inevitably have with their environment. We show how, in this relational interpretation, SSB for both lattice systems and (gauge) field theories should be understood as subtle, rather than spontaneous, symmetry breaking, still in contrast to explicit symmetry breaking. We also explain how algebraic definitions of SSB for infinite systems relate to the intuitive picture of SSB in finite systems and illustrate how asymptotic boundary conditions push the environment "to infinity". In this way, our relational interpretation of SSB provides a unified conceptual framework applicable to symmetry-breaking in systems of any size.