Abstract
A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian wavefunctionals for which expectation values of local operators can be efficiently calculated analytically and in a closed form. The method consists of a series of scale-dependent nonlinear canonical transformations on the fields of the theory under consideration. Here, the $\lambda\, \phi^4$ and the sine-Gordon scalar theories are used to illustrate how non-perturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory.
Highlights
In recent years, tensor networks, a new and powerful class of variational states, have proved to be very useful in addressing both static and dynamical aspects of a wide number of interacting many-body systems
Tensor networks, a new and powerful class of variational states, have proved to be very useful in addressing both static and dynamical aspects of a wide number of interacting many-body systems. They represent a class of systematic variational ansätze which, through the Rayleigh-Ritz variational principle, provide an elegant approximation to the ground state of an interacting theory by systematically identifying those degrees of freedom that are relevant for observable physics
The method uses a class of nonlinear canonical transformations which are applied to a Gaussian wave functional
Summary
Tensor networks, a new and powerful class of variational states, have proved to be very useful in addressing both static and dynamical aspects of a wide number of interacting many-body systems. A continuous version of MERA, known as cMERA, was proposed in [2] for free field theories It consists of building a scale-dependent representation of the ground state wave functional through a scale-dependent linear canonical transformation of the fields of the theory. The renormalization in scale is generated by a quadratic operator, and the resulting state is given by a Gaussian wave functional. Χ0Þ þ i pffiωffiffiffiΛffiffi π ðpÞ jΩIRi 1⁄4 0; ð3Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for all p, where ωΛ 1⁄4 Λ2 þ m2 with m the mass of the particles in the free theory, it is possible to show that the cMERA ansatz with a quadratic entangler is equivalent to the Gaussian wave functional given by.
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