Related papers: Topological field theory of dynamical systems
The raise of the symmetry breaking mechanism by Landau[1] is a landmark in the studies of phase transitions. The Kosterlitz-Thouless phase transition[2-3] and the fractional quantum Hall effect[4], however, are believed to be induced by…
Strongly correlated quantum many-body systems at low dimension exhibit a wealth of phenomena, ranging from features of geometric frustration to signatures of symmetry-protected topological order. In suitable descriptions of such systems, it…
A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that…
We introduce and study a disorder-free version of the quantum breakdown model with all-to-all interactions. The Hamiltonian factorizes into the product of the zero-momentum-mode occupation number and a quadratic Hamiltonian including only…
The spontaneous breaking of a global discrete translational symmetry in the finite, lattice quantum sine-Gordon model is demonstrated by a density matrix renormalization group. A phase diagram in the coupling constant - inverse system size…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
Static topologically-nontrivial configurations in sigma-models, for spatial dimension D \geq 2, are unstable. The question addressed here is whether such sigma-model solitons can be stabilized by steady rotation in internal space; that is,…
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
The dynamical behaviour of domain boundaries between different realizations of the vacuum of scalar fields with spontaneously broken phases is investigated. They correspond to zero-modes of the Goldstone fields, moving with the speed of…
Motivated by the recent introduction of a $U(1)$-symmetric toric code model, we investigate symmetry-based deformations of topological order by systematically deconstructing the Gauss-law-enforcing star terms of the toric code (TC)…
We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time…
We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere $S_F^2$. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform…
Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…
We put forward a proposal for topological quantum critical points (tQCPs) separating non-invertible chiral topological orders in $(2+1)$ dimensions. We conjecture that these tQCPs can be captured by a family of scale-invariant field…
We investigate aspects of non-equilibrium dynamics of strongly coupled field theories within holography. We establish a hydrodynamic description for anomalous quantum field theories subject to a strong external field for the first time in…
A one-dimensional driven two-species model with parallel sublattice update and open boundaries is considered. Although the microscopic many-body dynamics is symmetric with respect to the two species and interactions are short-ranged, there…
We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the…
We study nonequilibrium dynamics of relativistic $N$-component scalar field theories in Minkowski space-time in a classical-statistical regime, where typical occupation numbers of modes are much larger than unity. In this strongly…