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Tuesday, May 19th 2015

4:30 pm:

It is well known that spontaneous symmetry breaking can only take place in the thermodynamic limit. Yet, by general hydrodynamic and effective field theory arguments, fingerprints of this symmetry breaking are already encoded in finite volume system realizations. Here, I will discuss how to dig out these fingerprints in exact low-energy spectra of finite-size systems, a method which has been extremely successful over the last 20 years (starting e.g. with the first ‘numerical proof’ of long-range magnetic ordering in the 2D triangular antiferromagnet). The power of this method is not about system-size extrapolations (‘large enough’ system sizes are anyway quickly unreachable for many strongly correlated systems), but on the full exploitation of symmetry, which gives very stringent predictions for the structure and the exact content of the low-energy spectra. The underlying principles offer one of the most direct ways to understand the mechanism of spontaneous symmetry breaking, and as such it is a general and fundamental topic that goes beyond numerical simulations.

References:

[1] P. W. Anderson, PRB 86, 694 (1952)

[2] C. Lhuillier, cond-mat/0502464v1, chapter 2

[3] B. Bernu et al, PRL 69, 2590 (1992); PRB 50, 10048 (1994)

[4] P. Azaria et al, PRL 70, 2483 (1993)

[5] H. Neuberger and T. Ziman, PRB 39, 2608 (1989)

[6] P. Hasenfratz and F. Niedermayer, Z. Phys. B 92, 91-112 (1993)

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