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.
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.
The theory of spontaneous symmetry breaking---one of the cornerstones of modern condensed-matter physics---underlies the connection between a classically ordered object in the thermodynamic limit and its microscopic quantum-mechanical constituents. However, a large, but not infinitely large, system requires a finite symmetry-breaking perturbation to stabilize a symmetry-broken state over the exact quantum-mechanical ground state, respecting the symmetry. Here, we use the example of a particular antiferromagnetic model system to show that no matter how slowly such a symmetry-breaking perturbation is driven, the adiabatic limit can never be reached. Dynamically induced collective excitations---``quantum defects''---preempt the symmetry-breaking phenomenon and trigger the appearance of a symmetric nonequilibrium state that recursively collapses into the classical equilibrium state, breaking the symmetry at punctured times. The presence of this state allows ``quantum-classical'' transitions to be investigated and controlled in mesoscopic devices by externally supplying a proper dynamical symmetry-breaking perturbation.
During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in the thermodynamic limit was addressed in a recent paper proposing that the unitarity of quantum mechanical time evolution in macroscopic objects may be susceptible to a spontaneous breakdown. Here we will discuss the implications of this theory of spontaneous unitarity breaking for the modern experiments involving truly macroscopic Schrodinger cat states.
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.
Beginning with Anderson (1972) , spontaneous symmetry breaking ( ssb ) in infinite quantum systems is often put forward as an example of (asymptotic) emergence in physics , since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states (or equilibrium states at low temperature), although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect (viz. ssb ) seems theoretically recovered only in some idealisation (namely the thermodynamic limit), disappearing as soon as the idealisation is removed. We review the well-known arguments that (at first sight) no finite system can exhibit ssb , using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics (which typically forbids ssb ) versus classical mechanics (which allows it). This discrepancy between formalism and reality is quite similar to the measurement problem (now regarded as an instance of asymptotic emergence), and hence we address it in the same way, adapting an argument of the Landsman and Reuvers (2013) that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to (asymmetric) perturbations of the (symmetric) dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle (at least in this particularly threatening case).
The subject of condensed matter physics is very rich — there are an infinite number of parameters producing a diversity of exciting phenomena. As a theorist, my goal is to distill general principles out of this complexity — to construct theories that can coherently explain many known examples altogether.This thesis is composed of several attempts to develop such theories in topics related to spontaneously symmetry breaking. A remarkable feature of many-body interacting systems is that although they are described by equations respecting various symmetries, they may spontaneously organize into a state that explicitly breaks symmetries. Examples are numerous: various types of crystalline and magnetic orders, Bose-Einstein condensates of cold atoms, superfluids of liquid helium, chiral symmetry in QCD, neutron stars, and cosmic inflation.These systems with spontaneously broken continuous symmetries have gapless excitations, so called Nambu-Goldstone bosons (NGBs). Although the properties of NGBs are well understood in Lorentz-invariant systems, surprisingly, some basic properties of NGBs such as their number and dispersion in nonrelativistic systems have not been discussed from a general perspective. In the first part of this thesis, we solve this issue by developing and analyzing an effective Lagrangian that coherently captures the low-energy, long-distance physics of many different symmetry-breaking states all at once.Next, we examine whether these NGBs originating from spontaneous symmetry breaking remain to be well-defined excitations inside a metal, where low-energy electrons near Fermi surface can collide with them. Our result is a one equation criterion that specifies whether the interactions between electrons and NGBs can be ignored, or whether it completely changes their character. In the latter case, unusual phases of matter such as non-Fermi liquids may arise; in that case, NGBs are overdamped and cannot form particle-like excitations in spite of the assumed symmetry breaking.In the last part of this thesis, we investigate the possibility of spontaneously breaking of Hamiltonian itself. The homogeneity of time is one of the most fundamental symmetries of nature, underlying the conservation of the energy. The question is whether this symmetry can be spontaneously broken, as suggested recently by Wilczek, in analogy with ordinary crystals. Contrary to his proposal that attracted a significant attention and stimulated many further studies, we prove a no-go theorem that rules out spontaneously breaking of time translation, in the ground state or in the canonical ensemble of a general Hamiltonian.
The subject of condensed matter physics is very rich — there are an infinite number of parameters producing a diversity of exciting phenomena. As a theorist, my goal is to distill general principles out of this complexity — to construct theories that can coherently explain many known examples altogether.This thesis is composed of several attempts to develop such theories in topics related to spontaneously symmetry breaking. A remarkable feature of many-body interacting systems is that although they are described by equations respecting various symmetries, they may spontaneously organize into a state that explicitly breaks symmetries. Examples are numerous: various types of crystalline and magnetic orders, Bose-Einstein condensates of cold atoms, superfluids of liquid helium, chiral symmetry in QCD, neutron stars, and cosmic inflation.These systems with spontaneously broken continuous symmetries have gapless excitations, so called Nambu-Goldstone bosons (NGBs). Although the properties of NGBs are well understood in Lorentz-invariant systems, surprisingly, some basic properties of NGBs such as their number and dispersion in nonrelativistic systems have not been discussed from a general perspective. In the first part of this thesis, we solve this issue by developing and analyzing an effective Lagrangian that coherently captures the low-energy, long-distance physics of many different symmetry-breaking states all at once.Next, we examine whether these NGBs originating from spontaneous symmetry breaking remain to be well-defined excitations inside a metal, where low-energy electrons near Fermi surface can collide with them. Our result is a one equation criterion that specifies whether the interactions between electrons and NGBs can be ignored, or whether it completely changes their character. In the latter case, unusual phases of matter such as non-Fermi liquids may arise; in that case, NGBs are overdamped and cannot form particle-like excitations in spite of the assumed symmetry breaking.In the last part of this thesis, we investigate the possibility of spontaneously breaking of Hamiltonian itself. The homogeneity of time is one of the most fundamental symmetries of nature, underlying the conservation of the energy. The question is whether this symmetry can be spontaneously broken, as suggested recently by Wilczek, in analogy with ordinary crystals. Contrary to his proposal that attracted a significant attention and stimulated many further studies, we prove a no-go theorem that rules out spontaneously breaking of time translation, in the ground state or in the canonical ensemble of a general Hamiltonian.