ترغب بنشر مسار تعليمي؟ اضغط هنا

Holographic Symmetries and Generalized Order Parameters for Topological Matter

58   0   0.0 ( 0 )
 نشر من قبل Emilio Cobanera
 تاريخ النشر 2012
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance is that of {em holographic symmetry}. It reflects situations wherein global symmetries become, under a duality mapping, symmetries that act solely on the systems boundary. Holographic symmetries are naturally related to edge modes and localization. The utility of our approach is illustrated by systematically deriving generalized order parameters for pure and matter-coupled Abelian gauge theories, and for some models of topological matter.



قيم البحث

اقرأ أيضاً

We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological qu antum field theories (TQFTs). By formulating the order parameters in the Hilbert space of state sum TQFT, we establish the connection between the quantized non-local order parameters and the underlying field theory, clarifying the nature of the order parameters as topological invariants. We also formulate several entanglement measures including the entanglement negativity on state sum spin TQFT, and describe the exact correspondence of the entanglement measures to path integrals on a closed surface equipped with a specific spin structure.
Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE), and compare the so obtained results with predictions fro m GHD. One cornerstone of GHD is the GGE averaged microscopic currents. They can be obtained using form factors. Discussed is also a second, completely orthogonal approach based on the availability of a self-conserved current.
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY m odels. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define persistence critical exponents and study how they are related to those critical exponents usually considered.
38 - Jaakko Nissinen 2020
We discuss the higher-order topological field theory and response of topological crystalline insulators with no other symmetries. We show how the topology and geometry of the system is organised in terms of the elasticity tetrads which are ground sta te degrees of freedom labelling lattice topological charges, higher-form conservation laws and responses on sub-dimensional manifolds of the bulk system. In a crystalline insulator, they classify higher-order global symmetries in a transparent fashion. This coincides with the dimensional hierarchy of topological terms, the multipole expansion, and anomaly inflow, related to a mixed number of elasticity tetrads and electromagnetic gauge fields. In the continuum limit of the elasticity tetrads, the semi-classical expansion can be used to derive the higher-order or embedded topological responses to global U(1) symmetries, such as electromagnetic gauge fields with explicit formulas for the higher-order quasi-topological invariants in terms of the elasticity tetrads and Greens functions. The topological responses and readily generalized in parameter space to allow for e.g. multipole pumping. Our simple results further bridge the recently appreciated connections between topological field theory, higher form symmetries and gauge fields, fractonic excitations and topological defects with restricted mobility elasticity in crystalline insulators.
We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exh ibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا