tag:blogger.com,1999:blog-5439168179960787195.post3808308051940850698..comments2019-12-06T21:22:02.847+10:00Comments on Condensed concepts: What is quantum matter?Ross H. McKenziehttp://www.blogger.com/profile/09950455939572097456noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5439168179960787195.post-47321224462880733482013-06-06T10:00:52.380+10:002013-06-06T10:00:52.380+10:00liquid water may be quantum matter, its structure ...liquid water may be quantum matter, its structure should be predicted with quantum effects.LIn Kehttps://www.blogger.com/profile/00247682100268896391noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-52494423336080419282013-06-06T07:48:29.153+10:002013-06-06T07:48:29.153+10:00Great post. I think the sound of a term is import...Great post. I think the sound of a term is important, and the term "Quantum Matter" provides us with a useful counterpoint to "Soft Matter" and "Biological Matter", the three making up the trio of emergent matter types. Of course, the division between the two is extremely fuzzy and no doubt, discoveries in the future will serve to blur the lines further, perhaps requiring new definitions. <br /><br />Of course, everything is quantum, and to my mind, it is quantum mechanics that provides a big part of the canvas on which emergence develops. Classical physics for exampls, is an emergent consequence of quantum mechanics that we take for granted, because this is the world we live in. Superconductivity is a beautiful example of how new kinds of macroscopic behavior (which require h finite), but which are nevertheless described by emergent classical physics, derive from quantum physics.<br /><br /> Piers Colemanhttps://www.blogger.com/profile/14595901752473864838noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-42113149202655129132013-05-27T12:32:04.463+10:002013-05-27T12:32:04.463+10:00Thanks to Peter for raising the important question...Thanks to Peter for raising the important question about levels of "quantum-ness".<br /><br />Thanks to HM for clarifying this, particularly for the specific case of gapped systems.<br /><br />HM, what do you think is the clearest article which discusses the distinction between SRE and LRE [i.e. short-range vs. long-range entanglement]?Ross H. McKenziehttps://www.blogger.com/profile/09950455939572097456noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-51574080836748211662013-05-25T07:25:25.482+10:002013-05-25T07:25:25.482+10:00There is actually a finer graduation of quantum-ne...There is actually a finer graduation of quantum-ness (along the lines discussed by Peter Armitage above) in the case of gapped states. Actually according to this, topological insulators are not examples of topological order.<br /><br />One can define the notions of long-range entangled (LRE) states and short-range entangled (SRE) states for gapped systems. A SRE state is a state in which the ground state can be deformed into a product-state (no entanglement) by step by step removing the entanglement locally (for example between nearby sites in a spin system). If a state cannot be turned into a product-state in this way, it is said to be LRE. <br /><br />There can exit many distinct LRE states which cannot be turned into each-other by changing the local entanglement structure. These distinct classes of states are known as topological order, fractional quantum Hall effect is one example here, another is gapped spin-liquids. Thus different classes of topological order is related to different patterns of (long range) entanglement, or different ways of being quantum.<br /><br />If one however considers states with symmetries, and only allow for removal of local entanglement that respects the symmetry, then SRE states can also be split into distinct classes. These are known as symmetry protected topological (SPT) states. SPT states generically have interesting edge states which are protected as long as the given symmetry is unbroken. Thus these states are also quantum, but less than LRE states.<br /><br />For example, the free-fermion topological insulators are SPT states. Meaning that they do not have LRE and topological order (no anyons/topological entanglement entropy, ground state degeneracy on torus etc.). They are only protected from becoming a product state by a symmetry (such as time-reversal symmetry). The same for their edge states.<br /><br />Another famous example of a SPT state, is the Haldane spin-1 chain. At the edge, it has spin-1/2 excitations which are protected by symmetry.<br /><br />Similar classification of quantum-ness of gapless states, using patterns of entanglement, seems much more tricky.HMhttps://www.blogger.com/profile/15133711515963714923noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-40428233272316257252013-05-24T15:29:41.852+10:002013-05-24T15:29:41.852+10:00I think there are various levels of quantumness th...I think there are various levels of quantumness that need to be confronted. As you say, at some level all matter is quantum. But there is a certain sense in which a superconductor is more quantum than a liquid crystal. In the former case there are physical observables that have hbar in it (flux quantum). Yet in both these cases one can describe a phase transition to the ordered state in terms of classical ginzburg landau theory. And there is a certain sense in which one can understand the occurence of the broken u(1) symmetry as that the superconductor's phase becomes a classical variable in the same sense that the magnetization of a ferromagnet is a classical variable. At the next level of quantum are systems like metals that can only be written as product states in certain bases (states like superconductors share somewhat these properties, but in a different fashion). And the final and most quantum of states of matter are those states that don't admit a product state description and are highly entangled. Examples of the latter are spin-liquid states.<br /><br />Finer gradation of quantum-ness are probably possible.Peter Armitagehttps://www.blogger.com/profile/11567089164372083820noreply@blogger.com