# Minimizing couplings in renormalization by preserving short-range mutual information

@article{Bertoni2022MinimizingCI, title={Minimizing couplings in renormalization by preserving short-range mutual information}, author={Christian Bertoni and Joseph M. Renes}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

The connections between renormalization in statistical mechanics and information theory are intuitively evident, but a satisfactory theoretical treatment remains elusive. We show that the real space renormalization map that minimizes long range couplings in the renormalized Hamiltonian is, somewhat counterintuitively, the one that minimizes the loss of short-range mutual information between a block and its boundary. Moreover, we show that a previously proposed minimization focusing on…

## References

SHOWING 1-10 OF 29 REFERENCES

### Optimal Renormalization Group Transformation from Information Theory

- Computer SciencePhysical Review X
- 2020

This work investigates analytically the RG coarse-graining procedure and the renormalized Hamiltonian, which the RSMI algorithm defines, and shows that a perfect RSMI coarse- graining generically does not increase the range of a short-ranged Hamiltonian in any dimension.

### Information geometric approach to the renormalisation group

- Physics
- 2015

We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set…

### Tensor Network Renormalization.

- Computer SciencePhysical review letters
- 2015

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a…

### The renormalization group via statistical inference

- Physics
- 2014

In physics, one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We…

### Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group

- Physics
- 1998

The relative entropy in two-dimensional Field Theory is studied for its application as an irreversible quantity under the Renormalization Group, relying on a general monotonicity theorem for that…

### Field theory entropy, the H theorem, and the renormalization group.

- PhysicsPhysical review. D, Particles and fields
- 1996

It is argued that as a consequence of a generalized $H$ theorem Wilsonian RG flows induce an increase in entropy and proposed the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions.

### Mutual information, neural networks and the renormalization group

- Computer Science, PhysicsArXiv
- 2017

This work demonstrates a machine-learning algorithm capable of identifying the relevant degrees of freedom of a system and executing RG steps iteratively without any prior knowledge about the system, and applies the algorithm to classical statistical physics problems in one and two dimensions.

### The renormalization group: Critical phenomena and the Kondo problem

- Physics
- 1975

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in…

### Renormalization Group Flows of Hamiltonians Using Tensor Networks.

- PhysicsPhysical review letters
- 2017

It is emphasized that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information.