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Optimal free descriptions of many-body theories

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ABSTRACT

Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. Although these systems are promising for technological applications, they also present conceptual challenges, as they require approaches beyond mean-field and perturbation theory. Here we develop a general framework for identifying the free theory that is closest to a given interacting model in terms of their ground-state correlations. Moreover, we quantify the distance between them using the entanglement spectrum. When this interaction distance is small, the optimal free theory provides an effective description of the low-energy physics of the interacting model. Our construction of the optimal free model is non-perturbative in nature; thus, it offers a theoretical framework for investigating strongly correlated systems.

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Interaction distance across the phase diagram of the quantum Ising model.(a) The FM and (b) the AFM model at system size L=16 with periodic boundary conditions. The interaction distance (log scale) takes non-negligible values only in the vicinity of the critical point and critical line which are sketched in red. The scaling behaviour of  along the dashed lines is given in Fig. 2.
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f1: Interaction distance across the phase diagram of the quantum Ising model.(a) The FM and (b) the AFM model at system size L=16 with periodic boundary conditions. The interaction distance (log scale) takes non-negligible values only in the vicinity of the critical point and critical line which are sketched in red. The scaling behaviour of along the dashed lines is given in Fig. 2.

Mentions: Minimizing the interaction distance over the phase diagram we find that decays with L away from critical regions as shown in Fig. 1, with the variational parameters {} converging exponentially (see Methods). Thus, the model can be faithfully described by a free theory in these regions of the phase diagram. The exceptions only occur infinitesimally close to the FM critical point and at the AFM classical critical point. This is remarkable because these models are non-integrable and a priori have strong quantum fluctuations due to all energy scales being comparable in magnitude.


Optimal free descriptions of many-body theories
Interaction distance across the phase diagram of the quantum Ising model.(a) The FM and (b) the AFM model at system size L=16 with periodic boundary conditions. The interaction distance (log scale) takes non-negligible values only in the vicinity of the critical point and critical line which are sketched in red. The scaling behaviour of  along the dashed lines is given in Fig. 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5382319&req=5

f1: Interaction distance across the phase diagram of the quantum Ising model.(a) The FM and (b) the AFM model at system size L=16 with periodic boundary conditions. The interaction distance (log scale) takes non-negligible values only in the vicinity of the critical point and critical line which are sketched in red. The scaling behaviour of along the dashed lines is given in Fig. 2.
Mentions: Minimizing the interaction distance over the phase diagram we find that decays with L away from critical regions as shown in Fig. 1, with the variational parameters {} converging exponentially (see Methods). Thus, the model can be faithfully described by a free theory in these regions of the phase diagram. The exceptions only occur infinitesimally close to the FM critical point and at the AFM classical critical point. This is remarkable because these models are non-integrable and a priori have strong quantum fluctuations due to all energy scales being comparable in magnitude.

View Article: PubMed Central - PubMed

ABSTRACT

Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. Although these systems are promising for technological applications, they also present conceptual challenges, as they require approaches beyond mean-field and perturbation theory. Here we develop a general framework for identifying the free theory that is closest to a given interacting model in terms of their ground-state correlations. Moreover, we quantify the distance between them using the entanglement spectrum. When this interaction distance is small, the optimal free theory provides an effective description of the low-energy physics of the interacting model. Our construction of the optimal free model is non-perturbative in nature; thus, it offers a theoretical framework for investigating strongly correlated systems.

No MeSH data available.


Related in: MedlinePlus