Starting from the (d + 1)-dimensional Lifshitz critical boson with dynamical exponent z = 2, we propose two nontrivial deformations that preserve the Rokhsar-Kivelson structure where the groundstate is encoded in an underlying, local d-dimensional QFT. Specializing to d = 1 spatial dimension, the first deformation maps the groundstate to the quantum harmonic oscillator, leading to a gap for the scalar. We study the resulting correlation functions, and find that Cluster Decomposition is restored. The special form of the groundstate allows to analytically compute the c-function for the entanglement entropy along a renormalization group (RG) flow for the wavefunction, which is found to be strictly decreasing as in conformal field theories (CFTs). From the entropic c-function, we obtain the corner term for the z = 2 Lifshitz critical boson in (2+1)D in the small angle limit. The second deformation is non-Gaussian and yields a groundstate described by SL(2, R)-conformal quantum mechanics. This deformation preserves the conformal spatial symmetry of the groundstate, and constrains the form of the correlators and entanglement entropy. As a byproduct of our calculations, we obtain explicit results for the capacity of entanglement in Lifshitz theories and discuss their interpretation. We also prove the separability of the reduced density matrix of two disconnected subsystems for real-valued RK wavefunctions, implying the vanishing of logarithmic negativity. Finally, we comment on the relations to certain stoquastic quantum spin chains, the Motzkin and Fredkin chains.
As is well known, qubits are the fundamental building blocks of quantum computers, and more generally, of quantum information. A major challenge in the development of quantum devices arises because the information content in any quantum state is rather fragile, as no system is completely isolated from its environment. Generally, such interactions degrade the quantum state, resulting in a loss of information.Topological edge states are promising in this regard because they are in ways more robust against noise and decoherence. But creating and detecting edge states can be challenging. We describe a composite system consisting of a two-level system (the qubit) interacting with a finite Su-Schrieffer-Heeger chain (a hopping model with alternating hopping parameters) attached to an infinite chain. In this model, the dynamics of the qubit changes dramatically depending on whether or not an edge state exists. Thus, the qubit can be used to determine whether or not an edge state exists in this model.
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