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Solving frustration-free spin systems.

N de Beaudrap¹, M Ohliger, T J Osborne

¹Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.

Physical Review Letters

|September 28, 2010

Summary

This summary is machine-generated.

Researchers found a new way to solve complex quantum many-body systems exactly. This method applies to frustration-free spin models and provides an exact solution for their ground states, advancing quantum simulation techniques.

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Area of Science:

Quantum Many-Body Physics
Condensed Matter Theory
Quantum Information

Background:

Solving quantum many-body systems is a major challenge in physics.
Frustration-free models offer a simplified yet relevant class of quantum systems.
Exact solutions are rare, especially for systems on arbitrary lattices.

Purpose of the Study:

To identify and characterize a broad class of exactly solvable quantum many-body systems.
To develop an exact method for finding the ground-state manifold of these systems.
To establish a connection between these models and entanglement entropy properties.

Main Methods:

Identification of natural frustration-free spin-1/2 nearest-neighbor Hamiltonians.
Utilizing tensor networks of isometries acting on symmetric subspaces.
Application of real-space renormalization techniques.

Main Results:

A large class of quantum many-body systems solvable exactly has been identified.
The entire ground-state manifold is found exactly using a tensor network approach.
These models satisfy an area law for entanglement entropy, confirming a novel class.
The method provides an effective ansatz for simulating nearly frustration-free models.

Conclusions:

Exact solutions for a wide range of frustration-free spin models are achievable.
The developed tensor network method offers an exact real-space renormalization.
The findings provide a new class of models obeying the area law and improve quantum simulations.