Related papers: Duality via Sequential Quantum Circuit in the Topo…
The proposition that band geometry alone can protect optical states against disorder has proven not merely theoretically elegant but experimentally incontrovertible. A key attribute of photonic topological systems is their capacity to…
According to the holographic principle, the information content assigned to a gravitational region is processed by its lower dimensional boundary. As an example setup compatible with this principle, the AdS/CFT correspondence relies on the…
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can…
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which…
We study the quantum dynamics of the Bose-Hubbard model on a ladder formed by two rings coupled by tunneling effect. By implementing the Bogoliubov approximation scheme, we prove that, despite the presence of the inter-ring coupling term,…
We demonstrate the emergence of a holographic dimension in a system of 2D non-interacting Dirac fermions placed on a torus, by studying the scaling of multipartite entanglement measures under a sequence of renormalisation group (RG)…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Finite-depth quantum circuits preserve the long-range entanglement structure in quantum states and map between states within a gapped phase. To map between states of different gapped phases, we can use Sequential Quantum Circuits which…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We…
The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of quantum indeterminacy, using what we call "hbar-polar…
M-theory compactified on S^7/Z_k allows for a four-dimensional, asymptotically AdS cosmology. The holographic dual consists of ABJM theory with a non-supersymmetric marginal deformation. At weak 't Hooft coupling the dual theory possesses a…
We argue that given holographic CFT$_1$ in some state with a dual spacetime geometry M, and given some other holographic CFT$_2$, we can find states of CFT$_2$ whose dual geometries closely approximate arbitrarily large causal patches of M,…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…