KITP - 1

Quantum Phase Transitions

Week 1. 10-14 January, 2004

Blogger: Piers Coleman

The idea behind these Blog pages is to provide some institutional memory for the workshop. During the four month period that this workshop will run, there will be few participants who will stay more than two months.
It is hoped that these brief summary pages. will provide a record of discussions that took place throughout the meeting, and will, at the same time, provide a brief summary of the online talks that you may view.

Organizational Meeting: meeting plan for workshop
Participants and their interests.
Discussion: open questions in quantum phase transitions
Seminar; Disorder effects and Nexus of Quantum Phase transitions in URu2Si2. John Mydosh.

Monday, 10th January. The meeting began amidst some of the fiercest rain storms experienced in Southern California for several decades. On the first day, Monday - highway 101 became blocked by a mudslide at La Conchita, which buried the small town causing several fatalities. The freeway did not open again until Friday, causing several arriving participants to make a detour through the Central Valley of several hundred miles via Santa Maria. Several of the arriving participants, including Thomas Vojta, John Mydosh and Brian Maple, were stranded in Ventura.

10am Tuesday, 11th January, porthole room.
Organizational Meeting

The porthole room overlooks the Pacific Ocean, and is an ideal venue for non-technical discussion. Present were Sasha Abanov, Dietrich Belitz, Piers Coleman, Kevin Ingersent, Ted Kirpatrick, Nikolai Prokoviev, Thomas Vojta, Hilbert von Lohneyson and Peter Young. We took the occasion to discuss the seminar plan for the workshop. The following basic set up was agreed apon:

Daily: 10am. Common Room. Coffee and discussion.

(An informal venue for meeting and discussion.)

Monday: 10am. Auditorium. Blackboard Theory Discussion and Seminar

(No transparencies or powerpoint.)

Tuesday: 12.30pm. Auditorium. Main seminar.

(Bring your lunch.)

Thursday: 4.30pm. Founders Room. Informal discussion.

(Raise open questions, work done at meeting.)

We took the occasion to introduce ourselves and to mention key problems and ideas that fascinate us.
(See below).
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Participants present. Click on participant to read questions that they have posed.

Abanov, Sasha
Belitz, Dietrich
Buyers, Bill
Coleman, Piers
Ingersent, Kevin
Kirkpatrick, Ted

Mydosh, John
Prokofiev, Nikolai
Sushkov, Oleg
Vojta, Thomas
von Lohneyson, Hilbert
Young, Peter

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4.30pm Thursday, 13th January, Founders Room.
Discussion: open questions in quantum phase transitions

Present at this discussion were Dietrich Belitz, Bill Buyers, Piers Coleman, Kevin Ingersent, Ted Kirkpatrick, John Mydosh, Thomas Vojta, Hilbert von Loheyson and Peter Young. We decided to try to write down a list of open questions for discussion. Discussion spanned a wide range of quantum phase transitions, and the experimentalists present, Mydosh, Buyers and von Lohneyson worked hard to cast entire discussion in the context of real materials.

Here are the questions as they appeared on the blackboard:

Do we understand the thermodynamics and the electron transport at Ferromagnetic Quantum Critical points?

Dietrich Belitz drew, what is believed to be the generic phase diagram for the quantum phase transition of ferromagnetic systems, including a tri-critical point and two field-induced, quantum critical end points.

Systems mentioned were MnSi, ZrZn2, UGe2, Sr3Ru2O7

URu2Si2 may be also be in this category.

Belitz stated that yes, there was now a complete theory for the thermodynamics of the FM quantum critical point. He cited joint with with Kirpatrick and Rollbuehler .

In discussion, it came out that there is no equivalent of the epsilon expansion for the FM
QCP - that the leading order loops are always deceptive. Belitz claimed however, that one can, due to special properties of the problem (blogger: Ward identities?), one could nevertheless resum all the relevant diagrams.

But for the transport, there is much greater uncertainty. Do the naive transport exponents
are T^5/3 in 3D and T^4/3 in 2D agree (Millis, Schofield, Lonzarich and Grigera) with experiment?

Does Quantum Landau Ginzburg Theory ("Moriya-Hertz-Millis") account for the antiferromagnetic, heavy electron quantum critical points?

Here, there may be two classes of material - the "good" and "bad" actors. In the former,
specific heat is not so singular, and the resistivity fits the naive powers obtained by averaging the scattering rate (as opposed to the scattering time) over the Fermi surface. In the latter,
the resistivity is closer to linear, the specific heat displays a log, or faster than log
divergence, anomalous exponents have been observed in the susceptibililty and the Gruneissen parameter

Good	Bad
CeNi2Ge2 (Ce,La)Ru2Si2	Ce(Cu,Au)6 YbRh2Si2 CeCoIn5

Could it be that the former are well described by a quantum spin density wave, whereas the
latter involve a mixture of the physics of electron localization (Kondo) and magnetization?

If Quantum Landau Ginzburg fails - what replaces it?

Are there robust disorder effects at a quantum phase transition?

John Mydosh and Hilbert von Lohneyson emphasized the perils of mis-interpreting results that are driven by poor sample quality. Mydosh talked more at length on this in his Friday talk.

Having terrified the theorists about how much of the data may be due to uncontrolled disorder effects, Thomas Vojta proposed this question. Presumeably, all the strongly disordered
heavy electron quantum critical points would lie under this heading. We will hear more about this from Brian Maple and Meigan Aronson.

Thomas Vojta raised the question about whether one could produce a controlled understanding of Grifitths phases.

Is there a common origin to the T-linear resistivity and the T² Hall angle in the normal state of optimally doped high temperature superconductors and quantum critical heavy electron systems?

This is a way of framing, or disguising the question about whether the normal phase of the cuprates is driven by a quantum critcal point that hides beneath the superconducting dome.
The linear resistivity and T² Hall angle seen in YbRh2Si2 and CeCoIn5 are strongly remiscent of the cuprates at optimal doping. In the heavy electron case, they are most likely, driven by a quantum critical point. We don't understand either phenomenon at all.

What are the experimental realizations of quantum critical points and quantum phase transitions in insulating magnetic systems?

Theoretically, the transverse field Ising model is the most well understood model of a quantum critical point. There was a lengthy discussion of whether this has been effectively realized in
real systems. Systems discussed included:

LiHoF4. The only concrete realization to date of a transverse field Ising model.
(Pr, La)3Th. An old system, in which La doping appears to produce a QPT into the paramagnet.
(Eu,Sr)S In which at 50% Strontium doping, there is a spin glass which nests between the paramagnet and the Ferromagnet.
(Pd,Ni) Which was once thought to have a Ferromagnetic quantum critical point, but which is no longer thought to be so.

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10am Friday, 14th January. Auditorium.
Seminar; Disorder effects in heavy electron materials and the Nexus of Quantum Phase transitions in URu₂Si₂. John Mydosh.

Mydosh spent the first part of the talk discussing "unintentional disorder", focussing on URu2Ge2, where the disorder between Rh and Ge layers, to a level of 10%, completely wipes out the coherence peak in the resistivity. Mydosh suggested that these systems were closer to metallic glasses than to Kondo systems. He then turned to UPt_2Si_2, in which the unintentional disorder gives rise to a spin-glass remnant to the susceptibility. In this system, the resistivity does have a down-turn as antiferromagnetism develops. He drew a very nice phase diagram for the combined effects of doping and pressure.
In the second part of the talk, Mydosh talked about the field - temperature phase diagram of URu2Si2. He talked about the mysterious phase II which appears to hide a quantum phase transition.
When the system is doped with Rhodium, the phase diagram simplifies, wiping out the hidden order at low fields, leaving only phase II.	Buyers suggested that phase II, with its 1/3rd of saturation magnetization, involved layers of spins, 2/3rds up and 1/3rd down. Fisher and Coleman argued about whether the hidden critical point was a ferromagnetic quantum critical end point.

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